Combinatorial Proofs of Identities of Alzer and Prodinger and Some Generalizations

Authors

John Engbers, Marquette UniversityFollow
Christopher Stocker, Marquette UniversityFollow

Document Type

Article

Language

eng

Publication Date

5-25-2018

Publisher

Walter de Gruyter

Source Publication

Integers

Source ISSN

1867-0652

Abstract

We provide combinatorial proofs of identities published by Alzer and Prodinger. These identities include that for integers b, n, and r with b ≥ 1 and n − 1 ≥ r ≥ 0 we have

and for integers b, n, and r with b ≥ 0 and n − 1 ≥ r ≥ 0 we have

Our combinatorial proofs generalize squares to sth powers, and involve generalized Eulerian numbers and generalized Delannoy numbers.

Comments

Published version. Integers Vol. 18 (2018): #A49. Publisher link.© 2018 Wlater de Gruyter. Used with permission.

Recommended Citation

Engbers, John and Stocker, Christopher, "Combinatorial Proofs of Identities of Alzer and Prodinger and Some Generalizations" (2018). Mathematics, Statistics and Computer Science Faculty Research and Publications. 586.
https://epublications.marquette.edu/mscs_fac/586