Basic Bernoulli and Euler Polynomials and Numbers and q-Zeta Function

2003 ◽  
pp. 263-292
Author(s):  
Sergei K. Suslov
Keyword(s):  
Zeta Function ◽  
Euler Polynomials ◽  
Euler Polynomials And Numbers

scholarly journals NOTE ON q-DEDEKIND-TYPE SUMS RELATED TO q-EULER POLYNOMIALS

2011 ◽  
Vol 54 (1) ◽  
pp. 121-125 ◽  
Author(s):  
TAEKYUN KIM
Keyword(s):  
Continuous Function ◽  
Zeta Function ◽  
Higher Order ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Euler Numbers And Polynomials ◽  
Euler Polynomials And Numbers

AbstractRecently, q-Dedekind-type sums related to q-zeta function and basic L-series are studied by Simsek in [13] (Y. Simsek, q-Dedekind type sums related to q-zeta function and basic L-series, J. Math. Anal. Appl. 318 (2006), 333–351) and Dedekind-type sums related to Euler numbers and polynomials are introduced in the previous paper [11] (T. Kim, Note on Dedekind type DC sums, Adv. Stud. Contem. Math. 18 (2009), 249–260). It is the purpose of this paper to construct a p-adic continuous function for an odd prime to contain a p-adic q-analogue of the higher order Dedekind the type sums related to q-Euler polynomials and numbers by using an invariant p-adic q-integrals.

scholarly journals Zeros of Analytic Continuedq-Euler Polynomials andq-Euler Zeta Function

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
C. S. Ryoo
Keyword(s):  
Zeta Function ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Interesting Phenomenon

We study that theq-Euler numbersEn,qandq-Euler polynomialsEn,q(x)are analytic continued toEq(s)andEq(s,w). We investigate the new concept of dynamics of the zeros of analytic continued polynomials. Finally, we observe an interesting phenomenon of ‘‘scattering’’ of the zeros ofEq(s,w).

scholarly journals On Multiple Interpolation Functions of the Nörlund-Typeq-Euler Polynomials

2009 ◽  
Vol 2009 ◽  
pp. 1-14 ◽  
Author(s):  
Mehmet Acikgoz ◽  
Yilmaz Simsek
Keyword(s):  
Zeta Function ◽  
Generating Functions ◽  
Euler Polynomials ◽  
Multiple Interpolation ◽  
Definition Of ◽  
Interpolation Functions

In (2006) and (2009), Kim defined new generating functions of the Genocchi, Nörlund-typeq-Euler polynomials and their interpolation functions. In this paper, we give another definition of the multiple Hurwitz typeq-zeta function. This function interpolates Nörlund-typeq-Euler polynomials at negative integers. We also give some identities related to these polynomials and functions. Furthermore, we give some remarks about approximations of Bernoulli and Euler polynomials.

scholarly journals Fourier expansion and integral representation generalized Apostol-type Frobenius–Euler polynomials

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Alejandro Urieles ◽  
William Ramírez ◽  
María José Ortega ◽  
Daniel Bedoya
Keyword(s):  
Fourier Series ◽  
Integral Representation ◽  
Zeta Function ◽  
Fourier Expansion ◽  
Series Representation ◽  
Hurwitz Zeta Function ◽  
Euler Polynomials ◽  
Genocchi Polynomials ◽  
Lerch Zeta Function ◽  
Rational Arguments

Abstract The main purpose of this paper is to investigate the Fourier series representation of the generalized Apostol-type Frobenius–Euler polynomials, and using the above-mentioned series we find its integral representation. At the same time applying the Fourier series representation of the Apostol Frobenius–Genocchi and Apostol Genocchi polynomials, we obtain its integral representation. Furthermore, using the Hurwitz–Lerch zeta function we introduce the formula in rational arguments of the generalized Apostol-type Frobenius–Euler polynomials in terms of the Hurwitz zeta function. Finally, we show the representation of rational arguments of the Apostol Frobenius Euler polynomials and the Apostol Frobenius–Genocchi polynomials.

scholarly journals A Note on a New Type of Degenerate poly-Euler Numbers and Polynomials

2020 ◽  
Author(s):  
Waseem Khan
Keyword(s):  
Arithmetic Function ◽  
Bernoulli Numbers ◽  
Euler Polynomials ◽  
Euler Numbers ◽  
Polylogarithm Function ◽  
Euler Numbers And Polynomials ◽  
Special Numbers And Polynomials ◽  
Euler Polynomials And Numbers ◽  
New Type ◽  
Logarithm Function

Kim-Kim [12] introduced the new type of degenerate Bernoulli numbers and polynomials arising from the degenerate logarithm function. In this paper, we introduce a new type of degenerate poly-Euler polynomials and numbers, are called degenerate poly-Euler polynomials and numbers, by using the degenerate polylogarithm function and derive several properties on the degenerate poly-Euler polynomials and numbers. In the last section, we also consider the degenerate unipoly-Euler polynomials attached to an arithmetic function, by using the degenerate polylogarithm function and investigate some identities of those polynomials. In particular, we give some new explicit expressions and identities of degenerate unipoly polynomials related to special numbers and polynomials.

scholarly journals Sums of Products of -Euler Polynomials and Numbers

2009 ◽  
Vol 2009 (1) ◽  
pp. 381324 ◽  
Author(s):  
Young-Hee Kim ◽  
Kyung-Won Hwang ◽  
Taekyun Kim
Keyword(s):  
Euler Polynomials ◽  
Euler Polynomials And Numbers ◽  
Sums Of Products
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