How to use symsum command for a function of two variables and two indices?

Can anyone help to write a code in MATLAB for the expression given below:

I have tried with the following but it doesn't work: syms x y k1 k2 M_series=symsum(gamma(k1+1).*gamma(k2+1).*(x.^k1).*(y.^k2)./(factorial(k1).*factorial(k2).*gamma(k1+k2+1)),k1,0,Inf,k2,0,Inf);

[Torsten]

How do you define gamma(0) ? Usually

gamma(0)

ans = Inf

[Sania Nizamani]

You are right. I have made correction.

[Torsten]

So since factorial(k1) = gamma(k1+1) and factorial(k2) = gamma(k2+1), these terms cancel out and you are left with

sum_i sum_j 1/(i+j)! * x^i * y^j

Is this correct ?

Answer 1

[Torsten]

syms x y i j
assume(i,'integer')
assume(j,'integer')
A = symsum(symsum(x^i*y^j/factorial(i+j),i,0,Inf),j,0,Inf)

A = 

x0 = 0:0.2:1;
y0 = 0:0.25:1;
[x0,y0] = meshgrid(x0,y0);
[n,m] = size(x0);
for i = 1:n
    for j = 1:m
       A0(i,j) = double(subs(A,[x,y],[x0(i,j),y0(i,j)]));
    end
end
surf(x0,y0,A0)

[Sania Nizamani]

@Torsten

Thank you so much.