Matlab Program to Implement Bessel Functions Assignment Solution.

BESSEL PRINCIPAL

function J = besselprincipal(n, z, terms)

z = double(z);

result = 0;

for k = 0:terms

denom = (factorial(k).*gamma(n+k+1));

if denom ~= Inf % If the denominator is n Inf, we do not consider the term since it is equal to zero

result = result + (-1/4 *z.^2).^k ./(factorial(k).*gamma(n+k+1));

end

end

result = result.*(1/2 .*z).^n;

J = result;

end

BESSEL HANKEL

function J = besselhankel(n, z)

X = z - (pi/2)*(n + 1/2);

m = 4*n^2;

P = 1 - (m-1).*(m-9)./(2*(8*z).^2) + (m-1).*(m-9).*(m-25).*(m-49)./(factorial(4).*(8*z).^4);

Q = (m-1)./(8.*z) - (m-1).*(m-9).*(m-25)./(factorial(3).*(8.*z).^3);

result = sqrt(2./(pi*z)).*(P.*cos(X) - Q.*sin(X));

J = result;

end