How to integrate besselk function with variable limits?

In short, the function I am trying to arrive at is:

So far I have this code,

double x;
y=0:.1:8;
  
inner = @(y) besselk(5/3,y);
f= @(x) integral(inner,x,Inf);
F= @(x) x*f(x);

Power= @(x)  (sqrt(3)*q^3 *B * sin(alpha)* F(x))/(2*pi*m*c^2);

but am struggling to actually plot F(x). Whenever I switch x to vary like x= 0:.1:8, I can't do the integral, but if I switch it to a double, I can't plot the function.

Answer 1

[Star Strider]

One option is to use the arrayfun function to do the integration (essentially a one-line implied for loop) —

% double x;
y=0:.1:8;
  
inner = @(y) besselk(5/3,y);
f= @(x) integral(inner,x,Inf);
F= @(x) x.*arrayfun(@(x)f(x),x);

Power= @(x)  (sqrt(3)*q^3 *B * sin(alpha)* F(x))/(2*pi*m*c^2);


figure
plot(y, F(y))

Warning: Reached the limit on the maximum number of intervals in use. Approximate bound on error is 1.8e+34. The integral may not exist, or it may be difficult to approximate numerically to the requested accuracy.

xlabel('y')
ylabel('F(y)')

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[Nicolas Lamb]

thank you very much, I see where the trouble stems from!

[Star Strider]

My pleasure!

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