How to write this function in MATLAB?

Help me write the function K in Matlab.

[Walter Roberson]

I see no reason for that function to be periodic. The function is defined over the square [-R,R], [-R,R] as being the besselh formula and is defined as being 0 outside of B(0,R), whatever that is. The value outside the square but inside B(0,R) is not defined.

[Walter Roberson]

syms x1 x2 R
KG = vpaintegral(vpaintegral(1i/4*besselh(0,5*(x1^2+x2^2)), x1, -R, R),x2,-R,R);

digits(8); KG3_8 = subs(KG,R,3);

Below 8 digits, it refuses to integrate. Even with 8 digits, it takes a fair time.

[Anh Thu]

@Walter Roberson

First, K is defined over the square G as the formula above and then I want to extend function K from G to R^2 as 2R-periodic function with respect to x1 and x2.

[Torsten]

F = @(r) 1i/4*besselh(0,5*r.^2).*r;
R = 1.0;
sol = 2*pi*integral(F,0,R)

[Walter Roberson]

Multiply the area of one period by the number of periods in each direction.

As "periodic" almost always means infinite number of periods, then you know that there are only two possible answers: either the area of each period is 0 and so the infinitely extended area would be 0, or else the area of each period is non-zero and so the infinitely extended area would be infinite. As an examination shows the area to be be non-zero and complex, the infinitely extended area would be a complex infinity.