No plot in double integral

Hi! I try to solve the double integral, but there is an empty plot. Could you please tell me, what is wrong? In MathCad this integral is solved well.

n=1;
t=1;
r=1;
s=0:0.1:5;

fun = @(x,z,k) (x.*exp(2*n*t.*x.^2)./sqrt(1-x.^2)).*(exp(-2*t.*z.^2).*besselj(0,z.*k.*x).*(1+(sqrt(-pi)./(z*r)).*(1+((z*r).^2)/2).*(erfi(z*r/2)).*(exp(-((z*r).^2)/4))));
f3 = arrayfun(@(k)integral2(@(x,z)fun(x,z,k),0,Inf,0,1),s)

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

Warning: Inf or NaN value encountered.

Warning: The integration was unsuccessful.

f3 = 1×51

NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN NaN

Cor = ((-2*r*sqrt(2*n*t)*exp(-2*n*t))/(pi*erf(sqrt(2*n*t))*(atan(r/(2*sqrt(2*t)))-sqrt(2*t)/(2*r*(1/4+2*t/(r^2))))))*f3;
plot(s,Cor,'g-');

[Torsten]

See above. Integral2 returns that the integral does not exist because Inf or NaN values were returned from fun.

Is it correct that you want to integrate fun with respect to x from 0 to Inf and with respect to z from 0 to 1 ? Or vice versa ?

[the cyclist]

Can you upload the formula you are trying to integrate, in math notation? Maybe a mistake was made in transcribing it into MATLAB.

[Walter Roberson]

Are you expecting complex values?

Maybe you wanted x to be limited to 0 1 and z to be 0 to infinity? You coded with x being 0 to infinity and z being 0 to 1

n=1;
t=1;
r=1;
syms x z k s real
fun = (x.*exp(2*n*t.*x.^2)./sqrt(1-x.^2)).*(exp(-2*t.*z.^2).*besselj(0,z.*k.*x).*(1+(sqrt(-pi)./(z*r)).*(1+((z*r).^2)/2).*(erfi(z*r/2)).*(exp(-((z*r).^2)/4))));
f3 = subs(int(int(fun,x,0,inf), z, 0, 1), k, s)

f3 = 

fun_zhalf = limit(subs(fun, k, 1), z, 1/2)

fun_zhalf = 

xlimited = limit(fun_zhalf, x, 1)

xlimited = 

case_to_plot = children(children(xlimited, 3),1)

case_to_plot = 

fplot(case_to_plot, [0 2])

xlimited = limit(fun_zhalf, x, 2)

xlimited = 

vpa(xlimited)

ans = 

[the cyclist]

I was surprised to see the explicitly imaginary

sqrt(-pi)

in the expression, which is what prompted me to ask to see the math notation version.

[Walter Roberson]

I did not notice that. I wonder what it would look like if you used sqrt(pi) instead?

n=1;
t=1;
r=1;
syms x z k s real
Pi = sym(pi);
fun = (x.*exp(2*n*t.*x.^2)./sqrt(1-x.^2)).*(exp(-2*t.*z.^2).*besselj(0,z.*k.*x).*(1+(sqrt(Pi)./(z*r)).*(1+((z*r).^2)/2).*(erfi(z*r/2)).*(exp(-((z*r).^2)/4))));
f3 = subs(int(int(fun,x,0,inf), z, 0, 1), k, s)

f3 = 

fun_zhalf = limit(subs(fun, k, 1), z, 1/2)

fun_zhalf = 

xlimited = limit(fun_zhalf, x, 1)

xlimited = 

case_to_plot = children(children(xlimited, 3),1)

case_to_plot = 

fplot(case_to_plot, [0 2])

xlimited = limit(fun_zhalf, x, 2)

xlimited = 

vpa(xlimited)

ans = 

You get rid of the real-valued portion of the function (at least at some values), but the complex portion remains.

[Hexe]

Dear all, thank you for your replies. Yes, there is an imaginary part where sqrt(pi). And you are right, the integration is from 0 to 1 for x and 0-Inf for z. The math form is attached.