scholarly journals An explicit formula for the generalized Bernoulli polynomials

1988 ◽  
Vol 130 (2) ◽  
pp. 509-513 ◽  
Author(s):  
H.M Srivastava ◽  
Pavel G Todorov
Keyword(s):  
Explicit Formula ◽  
Bernoulli Polynomials ◽  
Generalized Bernoulli Polynomials

scholarly journals Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials

2009 ◽  
Vol 2009 ◽  
pp. 1-8 ◽  
Author(s):  
Taekyun Kim ◽  
Seog-Hoon Rim ◽  
Byungje Lee
Keyword(s):  
Bernoulli Polynomials ◽  
Bernoulli Numbers ◽  
Bernoulli Numbers And Polynomials ◽  
Power Sums ◽  
Invariant Integral ◽  
Generalized Bernoulli Polynomials ◽  
Symmetric Properties

By the properties ofp-adic invariant integral onℤp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties ofp-adic invariant integral onℤp, we give some interesting relationship between the power sums and the generalized Bernoulli polynomials.

scholarly journals New results on the q-generalized Bernoulli polynomials of level m

2019 ◽  
Vol 52 (1) ◽  
pp. 511-522
Author(s):  
Alejandro Urieles ◽  
María José Ortega ◽  
William Ramírez ◽  
Samuel Vega
Keyword(s):  
Gamma Function ◽  
Bernstein Polynomials ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Algebraic Properties ◽  
Generalized Bernoulli Polynomials ◽  
Polynomial Class

AbstractThis paper aims to show new algebraic properties from the q-generalized Bernoulli polynomials B_n^{[m - 1]}(x;q) of level m, as well as some others identities which connect this polynomial class with the q-generalized Bernoulli polynomials of level m, as well as the q-gamma function, and the q-Stirling numbers of the second kind and the q-Bernstein polynomials.

scholarly journals A three-term recurrence formula for the generalized Bernoulli polynomials

2021 ◽  
Vol 39 (6) ◽  
pp. 139-145
Author(s):  
Mohamed Amine Boutiche ◽  
Ghania Guettai ◽  
Mourad Rahmani ◽  
Madjid Sebaoui
Keyword(s):  
Recurrence Formula ◽  
Bernoulli Polynomials ◽  
Higher Order ◽  
Explicit Formulas ◽  
Whitney Numbers ◽  
Generalized Bernoulli Polynomials

In the present paper, we propose some new explicit formulas of the higher order Daehee polynomials in terms of the generalized r-Stirling and r-Whitney numbers of the second kind. As a consequence, we derive a three-term recurrence formula for the calculation of the generalized Bernoulli polynomials of order k.

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