scholarly journals On the Values of the Weighted -Zeta and -Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-7
Author(s):  
T. Kim ◽  
S. H. Lee ◽  
Hyeon-Ho Han ◽  
C. S. Ryoo
Keyword(s):  
Zeta Functions ◽  
Bernoulli Numbers ◽  
Bernoulli Numbers And Polynomials ◽  
Weighted Functions

Recently, the modified -Bernoulli numbers and polynomials are introduced in (D. V. Dolgy et al., in press). These numbers are valuable to study the weighted -zeta and -functions. In this paper, we study the weighted -zeta functions and weighted -functions from the modified -Bernoulli numbers and polynomials with weight .

scholarly journals Some results on degenerate Daehee and Bernoulli numbers and polynomials

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Han Young Kim ◽  
Jongkyum Kwon
Keyword(s):  
Bernoulli Numbers ◽  
Bernoulli Numbers And Polynomials

scholarly journals New type of degenerate Daehee polynomials of the second kind

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Sunil Kumar Sharma ◽  
Waseem A. Khan ◽  
Serkan Araci ◽  
Sameh S. Ahmed
Keyword(s):  
Generating Function ◽  
Special Class ◽  
Stirling Numbers ◽  
Bernoulli Numbers ◽  
Higher Order ◽  
Bernoulli Numbers And Polynomials ◽  
New Type ◽  
Order Degenerate ◽  
Math Phys

Abstract Recently, Kim and Kim (Russ. J. Math. Phys. 27(2):227–235, 2020) have studied new type degenerate Bernoulli numbers and polynomials by making use of degenerate logarithm. Motivated by (Kim and Kim in Russ. J. Math. Phys. 27(2):227–235, 2020), we consider a special class of polynomials, which we call a new type of degenerate Daehee numbers and polynomials of the second kind. By using their generating function, we derive some new relations including the degenerate Stirling numbers of the first and second kinds. Moreover, we introduce a new type of higher-order degenerate Daehee polynomials of the second kind. We also derive some new identities and properties of this type of 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.

p-adic zeta functions and Bernoulli numbers

1982 ◽  
Vol 19 (2) ◽  
pp. 1186-1194 ◽  
Author(s):  
Yu. V. Osipov
Keyword(s):  
Zeta Functions ◽  
Bernoulli Numbers

scholarly journals A note on q-analogue of Hermite-poly-Bernoulli numbers and polynomials

2019 ◽  
Vol 23 (2) ◽  
pp. 1-16 ◽  
Author(s):  
Waseem Khan ◽  
Idrees Khan ◽  
Musharraf Ali
Keyword(s):  
Bernoulli Numbers ◽  
Bernoulli Numbers And Polynomials
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