AnswerBun.com

alternating sum with Barnes G functions

MathOverflow Asked by JM Landsberg on September 21, 2020

Let $G(n)=(n-2)!(n-3)!cdots 1!$ denote the Barnes G-function.
I am pretty sure that
$$
sum_{m=0}^{k^2-1}
(-1)^mbinom{k^2-1}m
frac{G(k+n-m+1)}{G(n-m+1)G(k+1)(k^2)!}
= n-2k^2-2k
$$
when $k$ is odd
and is
$n-frac 12(k^2-1)$ when $k$ is even,
but I lack a proof. I’d already be happy for some references for identities regarding the Barnes function, as this is all new to me.

Add your own answers!

Related Questions

Euler function summation

0  Asked on December 13, 2020 by andrej-leko

 

Ask a Question

Get help from others!

© 2022 AnswerBun.com. All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP, SolveDir