Complex root of nonlinear complex equation containing besselh

I need to find the complex number which will make the real part of the function and the imaginary part, both equals 0.

I have tried fsolve, cxroot(which is a function from this site) and an algorithm of my own based on elemenantary numerical analysis, but none of them works.

Something more, my equations contains besselh(0 and 1,1,k*x) where k is a constant and x a variable. x must be numerical to use besselh on matlab.

I only need one root, and I approximatively know where it is. Is there a solution?

[Walter Roberson]

If you show the formula then I might be able to find a solution.

[Liber-T]

The formula is:

f=@(beta,alpha)(-824633720832/48234645482322198383329688730889*(-35966364677844412060643141365348432564643402407012018670507508*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))+1383321718378631483720139171946256562516216855531063600133927944*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)+905753002794110398140874601196454631959657182438133956870144*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*alpha^2+32460215418252061580944037024835544952798697131197742448640*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*alpha^4+32460215418252061580944037024835544952798697131197742448640*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(0,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*alpha^4+5702470276179413855269910610323412434069182758418171035648*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*alpha^4+4899611560585766330353257587936*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(5/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))+905753002794110398140874601196454631959657182438133956870144*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*beta^2-905753002794110398140874601196454631959657182438133956870144*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*alpha^2-905753002794110398140874601196454631959657182438133956870144*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*beta^2+725142510966693586690873727860*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(5/2)*besselj(0,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))-5702470276179413855269910610323412434069182758418171035648*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*alpha^4-5702470276179413855269910610323412434069182758418171035648*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*beta^4+5702470276179413855269910610323412434069182758418171035648*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*beta^4+725142510966693586690873727860*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(5/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))+35966364677844412060643141365348432564643402407012018670507508*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))-34214821657076483131619463661940474604415096550509026213888*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*beta^2*alpha^2+58179289974154055696971234248542818169044416237*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)-732574268577393154528190288796178783307563008*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*beta^2+732574268577393154528190288796178783307563008*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*alpha^2-58179289974154055696971234248542818169044416237*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)+732574268577393154528190288796178783307563008*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta^2-732574268577393154528190288796178783307563008*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*alpha^2+34214821657076483131619463661940474604415096550509026213888*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*beta^2*alpha^2-1811506005588220796281749202392909263919314364876267913740288*i*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*beta*alpha+22809881104717655421079642441293649736276731033672684142592*i*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*beta^3*alpha-22809881104717655421079642441293649736276731033672684142592*i*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(0,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*beta*alpha^3-1465148537154786309056380577592357566615126016*i*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*beta*alpha+1465148537154786309056380577592357566615126016*i*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta*alpha+1811506005588220796281749202392909263919314364876267913740288*i*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*beta*alpha-22809881104717655421079642441293649736276731033672684142592*i*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*beta^3*alpha+22809881104717655421079642441293649736276731033672684142592*i*besselj(0,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)*besselj(1,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))*beta*alpha^3+4899611560585766330353257587936*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(5/2)*besselj(0,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b)+i*bessely(0,sqrt(Ko^2*Ed-(beta+i*alpha)^2)*b))*(besselj(1,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2-(beta+i*alpha)^2))*b))+204731614320037507530315536150987865556697115417879584112420315*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(0,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)+204731614320037507530315536150987865556697115417879584112420315*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)-5155824785135707484634378956113654987403508135016590653521920*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta^2+5155824785135707484634378956113654987403508135016590653521920*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*alpha^2+32460215418252061580944037024835544952798697131197742448640*besselj(1,13/8388608000*(-3518977533259495-23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312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(0,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta*alpha^3+69673307907239274018270058656347788174944759444783185981865984*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta*alpha-877303119412217675137698788388218197935416912803233693433856*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta^3*alpha+877303119412217675137698788388218197935416912803233693433856*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta*alpha^3-10311649570271414969268757912227309974807016270033181307043840*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta*alpha+129840861673008246323776148099342179811194788524790969794560*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta^3*alpha-129840861673008246323776148099342179811194788524790969794560*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta*alpha^3-10311649570271414969268757912227309974807016270033181307043840*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(0,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta*alpha+129840861673008246323776148099342179811194788524790969794560*i*besselj(1,13/8388608000*(-3518977533259495-23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224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*alpha^2+219325779853054418784424697097054549483854228200808423358464*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta^4+219325779853054418784424697097054549483854228200808423358464*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*alpha^4-1315954679118326512706548182582327296903125369204850540150784*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(0,13/8388608000*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b)+i*bessely(1,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*b))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta^2*alpha^2-1315954679118326512706548182582327296903125369204850540150784*i*besselj(1,13/8388608000*(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*besselj(1,3/1677721600*(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2))*(besselj(0,sqrt((Ko^2-(beta+i*alpha)^2))*b)+i*bessely(0,sqrt((Ko^2-(beta+i*alpha)^2))*b))*(besselj(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a)+i*bessely(0,sqrt((Ko^2*Ed-(beta+i*alpha)^2))*a))*(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)*beta^2*alpha^2/(309099377921442-17592186044416*beta^2-35184372088832*i*beta*alpha+17592186044416*alpha^2)^(1/2)/(5588516752819671-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(5/2)/(-3518977533259495-23776875224726312*i-70368744177664*beta^2-140737488355328*i*beta*alpha+70368744177664*alpha^2)^(1/2)));

where x=beta+i*alpha, beta and alpha are real number.

[Liber-T]

Ko=4.1917 Ed=4.52 and here I've changed besselh in a combination of i*bessely and besselj.

[Matt Fig]

Does either beta or alpha have a particular value you are interested in? You said you knew approximately where the root was, where is that? What is a and b?

[Walter Roberson]

Yikes! And you are sure this has a solution??

It seems to me likely that the exact value of Ko and Ed would have a lot of impact on the solution (if there is one.) It also appears to me that probably your original expression had a number of floating point numbers that got converted in to rational expressions -- is that correct?

[Matt Fig]

Also the values of a and b. I made an initial assumption for a and b, then got several roots, some real and some complex... But it would help if we were given a and b, and a ballpark for alpha and/or beta.

[Liber-T]

Sorry, I forgot a and b, a=0.013;b=0.015;.

For Walter, there is a lot of chance that you are right and that my nymbers got converted into rational numbers.

My root should be between: Beta: 8.9111 and 8.9121, alpha: -0.0016 and -0.0024.

I would really like to know how you find all your roots.

[Walter Roberson]

To be honest, what I see after I substitute in the known values, is a formula that is obviously numeric nonsense if evaluated to less than 54 decimal places, and _probably_ numeric nonsense to somewhere in the 120 decimal place range. Evaluating to that precision is, however, completely unjustified by the 2 decimal places of accuracy of Ed, a, and b.

[Andrew Newell]

Is there a stage in your calculations where the problem is simple to state? Perhaps you should go back to this point and find a more direct numerical method to solve it (if it's an ODE, for example, use an ODE solver).

[Matt Fig]

I agree with Walter's assessment. Even if taken at face-value, there seems to be no way the roots are in that range. For example, using the constants you provided:

[A,B]=meshgrid(linspace(-.00024,-.00016),linspace(8.9111,8.9121));

V = f(A,B); % f as you posted...

min(abs(V:))) % Find the minimum magnitude in V

ans =

5.9007e+051

This is not even close to zero! So either your function oscillates wildly in that range, or the range is bogus, or the function is bogus...

[Liber-T]

There seems to be a mistake in my formula then, but the formula comes from a determinant, and I've heard that I could directly solve the determinant by using det. But when I read in matlab's help, there is no clue on how to use det that way.

[Walter Roberson]

I had Maple search for a complex zero in the indicated range. After a number of hours of calculation it indicated that there is no zero there.

Matt, the function does not oscillate wildly, but it has a very steep gradient -- much too steep for any potential zero to be detected by the default number of linspace() steps.

Liber-T: if the formula comes from a determinant, then that would seem to imply that you are looking for places where the original matrix is *not* invertible ? If so then possibly there are better ways to calculate that.