On Sums of Powers of Arithmetic Progressions, and Generalized Stirling, Eulerian and Bernoulli numbers

Autor:	Lang, Wolfdieter
Rok vydání:	2017
Předmět:	Mathematics - Number Theory 11B68 11B73
Druh dokumentu:	Working Paper
Popis:	For finite sums of non-negative powers of arithmetic progressions the generating functions (ordinary and exponential ones) for given powers are computed. This leads to a two parameter generalization of Stirling and Eulerian numbers. A direct generalization of Bernoulli numbers and their polynomials follows. On the way to find the Faulhaber formula for these sums of powers in terms of generalized Bernoulli polynomials one is led to a one parameter generalization of Bernoulli numbers and their polynomials. Generalized Lah numbers are also considered. Comment: 28 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1707.04451 Zobrazit plný text záznamu View this record from Arxiv