csch
Symbolic hyperbolic cosecant function
Syntax
Description
Examples
Hyperbolic Cosecant Function for Numeric and Symbolic Arguments
Depending on its arguments, csch returns
floating-point or exact symbolic results.
Compute the hyperbolic cosecant function for these numbers. Because these numbers are
not symbolic objects, csch returns floating-point results.
A = csch([-2, -pi*i/2, 0, pi*i/3, 5*pi*i/7, pi*i/2])
A = -0.2757 + 0.0000i 0.0000 + 1.0000i Inf + 0.0000i... 0.0000 - 1.1547i 0.0000 - 1.2790i 0.0000 - 1.0000i
Compute the hyperbolic cosecant function for the numbers converted to symbolic objects.
For many symbolic (exact) numbers, csch returns unresolved symbolic
calls.
symA = csch(sym([-2, -pi*i/2, 0, pi*i/3, 5*pi*i/7, pi*i/2]))
symA = [ -1/sinh(2), 1i, Inf, -(3^(1/2)*2i)/3, 1/sinh((pi*2i)/7), -1i]
Use vpa to approximate symbolic results with floating-point
numbers:
vpa(symA)
ans = [ -0.27572056477178320775835148216303,... 1.0i,... Inf,... -1.1547005383792515290182975610039i,... -1.2790480076899326057478506072714i,... -1.0i]
Plot Hyperbolic Cosecant Function
Plot the hyperbolic cosecant function on the interval from -10 to 10.
syms x fplot(csch(x),[-10 10]) grid on
Handle Expressions Containing Hyperbolic Cosecant Function
Many functions, such as diff,
int, taylor, and rewrite,
can handle expressions containing csch.
Find the first and second derivatives of the hyperbolic cosecant function:
syms x diff(csch(x), x) diff(csch(x), x, x)
ans = -cosh(x)/sinh(x)^2 ans = (2*cosh(x)^2)/sinh(x)^3 - 1/sinh(x)
Find the indefinite integral of the hyperbolic cosecant function:
int(csch(x), x)
ans = log(tanh(x/2))
Find the Taylor series expansion of csch(x) around x =
pi*i/2:
taylor(csch(x), x, pi*i/2)
ans = ((x - (pi*1i)/2)^2*1i)/2 - ((x - (pi*1i)/2)^4*5i)/24 - 1i
Rewrite the hyperbolic cosecant function in terms of the exponential function:
rewrite(csch(x), 'exp')
ans = -1/(exp(-x)/2 - exp(x)/2)
Input Arguments
Version History
Introduced before R2006a
