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Article


Title

Unified (p, q)-Bernoulli-Hermite polynomials

Authors

Year of publication

2018

Published in

Fasciculi Mathematici

Journal year: 2018 | Journal number: nr 61

Article type

scientific article

Publication language

english

Keywords
EN
  • Bernoulli polynomials and Bernoulli numbers
  • generating functions
  • Gauss hypergeometric function
  • Hurwitz zeta function and Euler’s polynomials
Abstract

EN The Concepts of p-Bernoulli numbers Bn, p and p-Bernoulli polynomials Bn, p (x) are generalized to (p,q)-Bernoulli numbers Bn, p, q and (p,q)-Bernoulli polynomials Bn, p, q (x), respectively. Some properties, generating functions and Laplace hypergeometric integral representations of (p, q)-Bernoulli numbers Bn, p, q and (p, q)-Bernoulli polynomials Bn, p, q (x), are established. Unified (p, q)-Bernoulli-Hermite polynomials are defined by a generating function which aid in proving the generalizations of the results of Khan et al [8], Kargin and Rahmani [7], Dattoli [4] and Pathan [9]. Some explicit summation formulas and some relationships between Appell’s function F1, Gauss hypergeomtric function, Hurwitz zeta function and Euler’s polynomials are also given.

Pages (from - to)

125 - 141

DOI

0.1515/fascmath-2018-0022

License type

CC BY-NC-ND (attribution - noncommercial - no derivatives)

Full text of article

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Access level to full text

public

Points of MNiSW / journal

10.0

Points of MNiSW / journal in years 2017-2021

10.0

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