I asked a similar question a few weeks ago and received a most helpful response, but unfortunately I had inaccurately transcribed thespecified form of that double integral from a file presented in Microsoft Word. I shall be most grateful for the numerical evaluation of this difficult double integral here presented in unambiguous and correct Maple definition, for cases n=0 and n=1.
i1 := Int(exp(-(k^2*sinh(s)^2/(gam-I*k*cosh(s)) + I*k*(1-cosh(s)))*v)*Hypergeom([I/k],,I*k*v)*v^n, v=0..R/2);
Jn := 1/R*Int(sinh(s)*coth(s/2)^(2*I/k)/(gam-I*k*cosh(s))^5*i1, s=0..smax);
smax := 20; R := 1680; k := 1/4; gam := 1/2;
The preceding response seemed to have several Maple statements that were not actually involved in the solution, making it difficult to follow the applied scheme of that solution.
Thanks in advance, John Ogilvie