scholarly journals Multivariatep-Adic Fermionicq-Integral onℤpand Related Multiple Zeta-Type Functions

2008 ◽  
Vol 2008 ◽  
pp. 1-13 ◽  
Author(s):  
Min-Soo Kim ◽  
Taekyun Kim ◽  
Jin-Woo Son
Keyword(s):  
Generating Functions ◽  
Zeta Functions ◽  
Bernoulli Polynomials ◽  
Partial Answer ◽  
Euler Polynomials ◽  
Multiple Zeta

In 2008, Jang et al. constructed generating functions of the multiple twisted Carlitz's typeq-Bernoulli polynomials and obtained the distribution relation for them. They also raised the following problem:“are there analytic multiple twisted Carlitz's typeq-zeta functions which interpolate multiple twisted Carlitz's typeq-Euler (Bernoulli) polynomials?”The aim of this paper is to give a partial answer to this problem. Furthermore we derive some interesting identities related to twistedq-extension of Euler polynomials and multiple twisted Carlitz's typeq-Euler polynomials.

scholarly journals ON WITTEN MULTIPLE ZETA-FUNCTIONS ASSOCIATED WITH SEMI-SIMPLE LIE ALGEBRAS IV

2010 ◽  
Vol 53 (1) ◽  
pp. 185-206 ◽  
Author(s):  
YASUSHI KOMORI ◽  
KOHJI MATSUMOTO ◽  
HIROFUMI TSUMURA
Keyword(s):  
Zeta Function ◽  
Lie Algebras ◽  
Generating Functions ◽  
Zeta Functions ◽  
Bernoulli Polynomials ◽  
Root Systems ◽  
Previous Method ◽  
Meromorphic Continuation ◽  
Functional Relations ◽  
Multiple Zeta

AbstractIn our previous work, we established the theory of multi-variable Witten zeta-functions, which are called the zeta-functions of root systems. We have already considered the cases of types A2, A3, B2, B3 and C3. In this paper, we consider the case of G2-type. We define certain analogues of Bernoulli polynomials of G2-type and study the generating functions of them to determine the coefficients of Witten's volume formulas of G2-type. Next, we consider the meromorphic continuation of the zeta-function of G2-type and determine its possible singularities. Finally, by using our previous method, we give explicit functional relations for them which include Witten's volume formulas.

scholarly journals Some (p, q)-analogues of Apostol type numbers and polynomials

2019 ◽  
Vol 23 (1) ◽  
pp. 37-50 ◽  
Author(s):  
Mehmet Acikgoz ◽  
Serkan Araci ◽  
Ugur Duran
Keyword(s):  
Generating Functions ◽  
Bernoulli Polynomials ◽  
Euler Polynomials ◽  
New Class

We consider a new class of generating functions of the generalizations of Bernoulli and Euler polynomials in terms of (p, q)-integers. By making use of these generating functions, we derive (p, q)-generalizations of several old and new identities concerning Apostol–Bernoulli and Apostol–Euler polynomials. Finally, we define the (p, q)-generalization of Stirling polynomials of the second kind of order v, and provide a link between the (p, q)-generalization of Bernoulli polynomials of order v and the (p, q)-generalization of Stirling polynomials of the second kind of order v.

scholarly journals Some Properties of $Q$-Hermite Fubini Numbers and Polynomials

2019 ◽  
Author(s):  
Waseem A. Khan
Keyword(s):  
Generating Functions ◽  
Hermite Polynomials ◽  
Bernoulli Polynomials ◽  
Stirling Numbers ◽  
Euler Polynomials ◽  
New Class ◽  
Genocchi Polynomials ◽  
Summation Formulas

The main purpose of this paper is to introduce a new class of $q$-Hermite-Fubini numbers and polynomials by combining the $q$-Hermite polynomials and $q$-Fubini polynomials. By using generating functions for these numbers and polynomials, we derive some alternative summation formulas including powers of consecutive $q$-integers.  Also, we establish some relationships for $q$-Hermite-Fubini polynomials associated with $q$-Bernoulli polynomials, $q$-Euler polynomials and $q$-Genocchi polynomials and $q$-Stirling numbers of the second kind.

scholarly journals Degenerate Bell polynomials associated with umbral calculus

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Taekyun Kim ◽  
Dae San Kim ◽  
Han-Young Kim ◽  
Hyunseok Lee ◽  
Lee-Chae Jang
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Bernoulli Polynomials ◽  
Umbral Calculus ◽  
Bell Polynomials ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Type Formula ◽  
Euler Numbers And Polynomials ◽  
Special Numbers And Polynomials

Abstract Carlitz initiated a study of degenerate Bernoulli and Euler numbers and polynomials which is the pioneering work on degenerate versions of special numbers and polynomials. In recent years, studying degenerate versions regained lively interest of some mathematicians. The purpose of this paper is to study degenerate Bell polynomials by using umbral calculus and generating functions. We derive several properties of the degenerate Bell polynomials including recurrence relations, Dobinski-type formula, and derivatives. In addition, we represent various known families of polynomials such as Euler polynomials, modified degenerate poly-Bernoulli polynomials, degenerate Bernoulli polynomials of the second kind, and falling factorials in terms of degenerate Bell polynomials and vice versa.

scholarly journals Two types of hypergeometric degenerate Cauchy numbers

2020 ◽  
Vol 18 (1) ◽  
pp. 417-433
Author(s):  
Takao Komatsu
Keyword(s):  
Zeta Functions ◽  
Bernoulli Polynomials ◽  
Cauchy Numbers

Abstract In 1985, Howard introduced degenerate Cauchy polynomials together with degenerate Bernoulli polynomials. His degenerate Bernoulli polynomials have been studied by many authors, but his degenerate Cauchy polynomials have been forgotten. In this paper, we introduce some kinds of hypergeometric degenerate Cauchy numbers and polynomials from the different viewpoints. By studying the properties of the first one, we give their expressions and determine the coefficients. Concerning the second one, called H-degenerate Cauchy polynomials, we show several identities and study zeta functions interpolating these polynomials.

Periods, Multiple Zeta Functions and ζ(3)

2014 ◽  
pp. 185-203
Author(s):  
M. Ram Murty ◽  
Purusottam Rath
Keyword(s):  
Zeta Functions ◽  
Multiple Zeta

scholarly journals Certain results of hybrid families of special polynomials associated with appell sequences

Filomat ◽  
2019 ◽  
Vol 33 (12) ◽  
pp. 3833-3844 ◽  
Author(s):  
Ghazala Yasmin ◽  
Abdulghani Muhyi
Keyword(s):  
Generating Functions ◽  
Mixed Type ◽  
Bernoulli Polynomials ◽  
Operational Method ◽  
Appell Polynomials ◽  
Special Polynomials ◽  
Appell Sequences

In this article, the Legendre-Gould-Hopper polynomials are combined with Appell sequences to introduce certain mixed type special polynomials by using operational method. The generating functions, determinant definitions and certain other properties of Legendre-Gould-Hopper based Appell polynomials are derived. Operational rules providing connections between these formulae and known special polynomials are established. The 2-variable Hermite Kamp? de F?riet based Bernoulli polynomials are considered as an member of Legendre-Gould-Hopper based Appell family and certain results for this member are also obtained.

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