Higher-order Euler-type polynomials and their applications
نویسندگان
چکیده
منابع مشابه
Apostol-euler Polynomials of Higher Order and Gaussian Hypergeometric Functions
The purpose of this paper is to give analogous definitions of Apostol type (see T. M. Apostol [Pacific J. Math. 1 (1951), 161-167]) for the so-called Apostol-Euler numbers and polynomials of higher order. We establish their elementary properties, obtain several explicit formulas involving the Gaussian hypergeometric function and the Stirling numbers of the second kind, and deduce their special ...
متن کاملGeneralized q-Euler Numbers and Polynomials of Higher Order and Some Theoretic Identities
Copyright q 2010 T. Kim and Y. H. Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We give a new construction of the q-Euler numbers and polynomials of higher order attached to Dirichlet's character χ. We derive some theoretic...
متن کاملNote on q-Extensions of Euler Numbers and Polynomials of Higher Order
In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted (h, q)-extension of Euler polynomials and numbers, by using p-adic q-deformed fermionic integral on Zp. By applying their generating functions, they derived the complete sums of products of the twisted (h, q)-extension of Euler polynomials and numbers, see[13, 14]. In this paper we cosider the new q-extension o...
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Explicit expressions for restricted partition function W (s,d) and its quasiperiodic components Wj(s,d ) (called Sylvester waves) for a set of positive integers d = {d1, d2, . . . , dm} are derived. The formulas are represented in a form of a finite sum over Bernoulli and Euler polynomials of higher order with periodic coefficients. A novel recursive relation for the Sylvester waves is establis...
متن کاملOn the Twisted q-Analogs of the Generalized Euler Numbers and Polynomials of Higher Order
Let p be an odd prime number. For n ∈ Z N ∪ {0}, let Cpn {ζ | ζpn 1} be the cyclic group of order p, and let Tp limn→∞Cpn ⋃ n≥0 Cpn Cp∞ be the space of locally constant functions in the p-adic number fieldCp. When one talks of q-extension, q is variously considered as an indeterminate, a complex number q ∈ C, or p-adic number q ∈ Cp. If q ∈ C, one normally assumes that |q| < 1. If q ∈ Cp, one n...
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ژورنال
عنوان ژورنال: Fixed Point Theory and Applications
سال: 2013
ISSN: 1687-1812
DOI: 10.1186/1687-1812-2013-40