List questions from polygamma | MathQa

Closed form for $\sum_{n=1}^{\infty} \frac{1}{1+n+n^2+\cdots+n^a}$

Published on 03 Jan 2025 - 1:34

Minimizing $f(x)=A^{\frac{tx-1}{x-1}} \left( c^x \frac{\Gamma(0.5+x)}{\sqrt{\pi}} \right)^{\frac{1-t}{x-1}}$ subject to the constraint

Published on 12 Jan 2025 - 23:32

Closed form for $\sum_{n=0}^\infty\frac{\Gamma\left(n+\tfrac14\right)}{2^n\,(4n+1)^2\,n!}$

Published on 05 Jan 2025 - 12:15

Does this reduce down to the PolyGamma function?

Published on 12 Jan 2025 - 20:41

Closed Form for the Integral: $\int_0^1 t^n\log\Gamma(t+a)dt$

Published on 12 Jan 2025 - 20:49

Integral $\int_0^\infty\Big[\log\left(1+x^2\right)-\psi\left(1+x^2\right)\Big]dx$

Published on 12 Jan 2025 - 20:55

Show some properties of the Digamma Function

Published on 12 Jan 2025 - 20:39

Limit involving Polygamma function: $\lim_{x\to \infty} \sum_{k = 0}^\infty \frac{2x^2}{(x + k)^3}$

Published on 12 Jan 2025 - 20:58

Evaluation of a digamma series involving golden-ratio

Published on 12 Jan 2025 - 20:46

The limit of the ratio of polygamma functions

Published on 12 Jan 2025 - 20:39