Notes on generalization of the Bernoulli type polynomials

Kurt B., ŞİMŞEK Y.

APPLIED MATHEMATICS AND COMPUTATION, vol.218, no.3, pp.906-911, 2011 (SCI-Expanded, Scopus)

  • Publication Type: Article / Article
  • Volume: 218 Issue: 3
  • Publication Date: 2011
  • Doi Number: 10.1016/j.amc.2011.03.086
  • Journal Name: APPLIED MATHEMATICS AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.906-911
  • Keywords: Bernoulli numbers and polynomials, Euler polynomials, Apostol-Bernoulli polynomials, Apostol-Bernoulli polynomials of order alpha, Apostol-Euler polynomials, Consecutive sums, Generating function, Hurwitz-Lerch zeta functions, APOSTOL-BERNOULLI, EULER POLYNOMIALS, NUMBERS, FORMULAS, ZETA
  • Akdeniz University Affiliated: Yes

Abstract

Recently, Srivastava et al. introduced a new generalization of the Bernoulli, Euler and Genocchi polynomials (see [H.M. Srivastava, M. Garg, S. Choudhary, Russian J. Math. Phys. 17 (2010) 251–261] and [H.M. Srivastava, M. Garg, S. Choudhary, Taiwanese J. Math. 15 (2011) 283–305]). They established several interesting properties of these general polynomials, the generalized Hurwitz–Lerch zeta functions and also in series involving the familiar Gaussian hypergeometric function. By the same motivation of Srivastava’s et al. [11] and [12], we introduce and derive multiplication formula and some identities related to the generalized Bernoulli type polynomials of higher order associated with positive real parameters a, b and c. We also establish multiple alternating sums in terms of these polynomials. Moreover, by differentiating the generating function of these polynomials, we give a interpolation function of these polynomials.

Recently, Srivastava et al. introduced a new generalization of the Bernoulli, Euler and Genocchi polynomials (see [H. M. Srivastava, M. Garg, S. Choudhary, Russian J. Math. Phys. 17 (2010) 251-261] and [H. M. Srivastava, M. Garg, S. Choudhary, Taiwanese J. Math. 15 (2011) 283-305]). They established several interesting properties of these general polynomials, the generalized Hurwitz-Lerch zeta functions and also in series involving the familiar Gaussian hypergeometric function. By the same motivation of Srivastava's et al. [11,12], we introduce and derive multiplication formula and some identities related to the generalized Bernoulli type polynomials of higher order associated with positive real parameters a, b and c. We also establish multiple alternating sums in terms of these polynomials. Moreover, by differentiating the generating function of these polynomials, we give a interpolation function of these polynomials. Crown Copyright (C) 2011 Published by Elsevier Inc. All rights reserved.