1
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0answers
192 views

Convergence of $\sum_{n=1}^\infty \frac{\psi^{(1)}(1-n/\pi)}{n^3}$

Related to an open problem about another series. Set $$A= \sum_{n=1}^\infty \frac{\psi^{(1)}(1-n/\pi)}{n^3}$$ where $\psi^{(n)}(k)$ is the polygamma function. Does $A$ converge? The related ...
3
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0answers
216 views

Alternating sums of powers of the lngamma ($\small f_p(x) = \sum \log(k!)^p x^k $ at $\small x=-1$)

I'm still fiddling with this recent question and come to a detail, whether I can find closed forms for the sums of the $\small lngamma() $ function. Precisely $$ \small f_p(x) = \sum_{k=0}^{\infty} ...