Answer by honeybadger for Check the convergence of double sum
This is my attempt to prove that Sum 2 also converges.Let Sum 1 i.e. $\sum _{p=0}^{k-1} \left(\frac{\sqrt{\frac{(p+1) \Gamma \left(p+\frac{11}{4}\right)}{\Gamma (p+2)}}}{(p+2) \sqrt{\Gamma...
View ArticleAnswer by user64494 for Check the convergence of double sum
Despite your claim, Sum 1 diverges. Here are my arguments. First,Series[Sqrt[Gamma[7/4 + j]/(Gamma[11/4]*Gamma[1 + j])]/(Sqrt[j]*(j+ 1)),...
View ArticleCheck the convergence of double sum
I have the following double summations:Sum 1 : $\sum _{p=0}^{k-1} \left(\frac{\sqrt{\frac{(p+1) \Gamma \left(p+\frac{11}{4}\right)}{\Gamma (p+2)}}}{(p+2) \sqrt{\Gamma \left(\frac{11}{4}\right)}}-\sum...
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