Extended Bernoulli and Stirling matrices and related combinatorial identities

CAN M., DAĞLI M. C.

LINEAR ALGEBRA AND ITS APPLICATIONS, vol.444, pp.114-131, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 444
  • Publication Date: 2014
  • Doi Number: 10.1016/j.laa.2013.11.031
  • Journal Name: LINEAR ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.114-131
  • Keywords: Bernoulli polynomials, Stirling numbers, Hyperharmonic numbers, Pascal matrix, Bernoulli matrix, Stirling matrix, DEGENERATE BERNOULLI, LINEAR ALGEBRA, POLYNOMIALS
  • Akdeniz University Affiliated: Yes

Abstract

In this paper we establish plenty of number theoretic and combinatoric identities involving generalized Bernoulli polynomials and Stirling numbers of both kinds, which generalize various known identities. These formulas are deduced from Pascal type matrix representations of Bernoulli and Stirling numbers. For this we define and factorize a modified Pascal matrix corresponding to Bernoulli and Stirling cases. (C) 2013 Elsevier Inc. All rights reserved.