On the generalized Apostol-type Frobenius-Euler polynomials
04 Jan 2013-Advances in Difference Equations (Springer International Publishing)-Vol. 2013, Iss: 1, pp 1-9
TL;DR: In this article, the authors derived new identities related to the Frobenius-Euler polynomials and generalized Carliz's results. And they also gave a relation between the generalized Frobius Euler Polynomial and the generalized Hurwitz-Lerch zeta function at negative integers.
Abstract: The aim of this paper is to derive some new identities related to the Frobenius-Euler polynomials. We also give relation between the generalized Frobenius-Euler polynomials and the generalized Hurwitz-Lerch zeta function at negative integers. Furthermore, our results give generalized Carliz’s results which are associated with Frobenius-Euler polynomials. MSC:05A10, 11B65, 28B99, 11B68.
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Book•
30 Jun 2001
TL;DR: In this article, the Zeta and related functions are used to define the determinants of the Laplacians, and series of series involving Zeta Functions are used for series representation.
Abstract: Preface. Acknowledgements. 1. Introduction and Preliminaries. 2. The Zeta and Related Functions. 3. Series Involving Zeta Functions. 4. Evaluations and Series Representations. 5. Determinants of the Laplacians. 6. Miscellaneous Results. Bibliography. Author Index. Subject Index.
800 citations
Book•
08 Nov 2011
TL;DR: Zeta and q-Zeta Functions and Associated Series and Integrals as discussed by the authors is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions, which includes a new chapter on the theory and applications of the basic (or q-) extensions of various special functions.
Abstract: Zeta and q-Zeta Functions and Associated Series and Integrals is a thoroughly revised, enlarged and updated version of Series Associated with the Zeta and Related Functions. Many of the chapters and sections of the book have been significantly modified or rewritten, and a new chapter on the theory and applications of the basic (or q-) extensions of various special functions is included. This book will be invaluable because it covers not only detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions, but stimulating historical accounts of a large number of problems and well-classified tables of series and integrals. Detailed and systematic presentations of the theory and applications of the various methods and techniques used in dealing with many different classes of series and integrals associated with the Zeta and related functions
682 citations
Posted Content•
TL;DR: In this article, Wang et al. constructed uniform differentiable functions of the Bernoulli numbers and polynomials at negative integers, and proved analytic continuation of some basic (or $q$-) $L$% -series.
Abstract: By using $q$-Volkenborn integration and uniform differentiable on $\mathbb{Z}%_{p}$, we construct $p$-adic $q$-zeta functions. These functions interpolate the $q$-Bernoulli numbers and polynomials. The value of $p$-adic $q$-zeta functions at negative integers are given explicitly. We also define new generating functions of $q$-Bernoulli numbers and polynomials. By using these functions, we prove analytic continuation of some basic (or $q$-) $L$% -series. These generating functions also interpolate Barnes' type Changhee $% q $-Bernoulli numbers with attached to Dirichlet character as well. By applying Mellin transformation, we obtain relations between Barnes' type $q$% -zeta function and new Barnes' type Changhee $q$-Bernolli numbers. Furthermore, we construct the Dirichlet type Changhee (or $q$-) $L$% -functions.
195 citations