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.

0 Asked on December 15, 2020 by shaoyang-zhou

1 Asked on December 15, 2020

1 Asked on December 14, 2020 by nahila

2 Asked on December 10, 2020 by yada

1 Asked on December 9, 2020 by neothecomputer

ac commutative algebra algebraic number theory nt number theory ra rings and algebras

1 Asked on December 9, 2020 by mb2009

0 Asked on December 8, 2020 by dbcohsmoothness

ag algebraic geometry derived algebraic geometry derived categories homological algebra

1 Asked on December 7, 2020

1 Asked on December 7, 2020 by qsh

algebraic groups geometric group theory gr group theory linear algebra rt representation theory

0 Asked on December 6, 2020 by sharpe

0 Asked on December 6, 2020 by xindaris

at algebraic topology cohomology limits and colimits sheaf cohomology

0 Asked on December 6, 2020 by winawer

lie superalgebras mp mathematical physics reference request rt representation theory vertex algebras

1 Asked on December 5, 2020 by leo-herr

ag algebraic geometry algebraic curves birational geometry blow ups

1 Asked on December 4, 2020 by lyrically-wicked

1 Asked on December 4, 2020 by andrea-marino

calculus of variations connections differential topology geodesics transversality

0 Asked on December 3, 2020 by eric-yan

0 Asked on December 3, 2020 by user164740

ag algebraic geometry at algebraic topology complex geometry dg differential geometry gt geometric topology

2 Asked on December 1, 2020 by wolfgang

big picture co combinatorics modular forms special functions

2 Asked on December 1, 2020 by bernhard-boehmler

computer algebra finite groups gr group theory ra rings and algebras rt representation theory

Get help from others!

Recent Answers

- Jon Church on Why fry rice before boiling?
- Lex on Does Google Analytics track 404 page responses as valid page views?
- Peter Machado on Why fry rice before boiling?
- Joshua Engel on Why fry rice before boiling?
- haakon.io on Why fry rice before boiling?

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