Friday, 1 May 2015

sequences and series - Evaluating Sum involving binomial coefficients and powers

I would like to evaluate the double sum n=1m=1(n+m)!n!m!n2m2(12)n+m. My starting point was to consider n=1m=1(n+m)!n!m!xnym=11xy11x11y+1 |x|+|y|<1 All what is left is to divide by xy then integrate with respect to x and then with respect to y (process should be repeated twice) finally set x=y=12. I am however stuck in evaluating the resulting integrals. I expect logarithmic and polylogarithmic functions to show up in the final result. I would appreciate if you can help me formulating the value of this sum.
Thanks for your help...

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