I am trying to integrate an expression in terms of variables n and m in which I can substitute values in and sum to get a large number of terms. I am using the Raleigh-Ritz energy minimization principle. My initial funtions are:
w[x_,y_]:= C\_0 + C\_\(m,n\)*((2-Cos[2*Pi*n*x]-Cos[2*Pi*n*y]))^m
u[x_,y_]:= A\_0*Sin[2*Pi*x] + A\_\(m, n\)*Sin[2*Pi*n*x]*Cos[2*Pi*m*y]
The goal is to sum up these functions for say n=10 and m=10 so that each is multiplied by a constant term of subscript n,m. If i explicitely define all n=10 and m=10 the integration runs endlessly. Does anyone know a way to do the integration symbolically or if there is an easier way to go about this problem? Attached is an example program.
Attachment: example program.nb, URL: ,