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- Title
Some Results on Generalized Multi Poly-Bernoulli and Euler Polynomials.
- Authors
Jolany, Hassan; Mohebbi, Hossein; Alikelaye, R. Eizadi
- Abstract
The Arakawa-Kaneko zeta function has been introduced ten years ago by T. Arakawa and M. Kaneko in [22]. In [22], Arakawa and Kaneko have expressed the special values of this function at negative integers with the help of generalized Bernoulli numbers B(k) called poly-Bernoulli numbers. Kim-Kim [4] introduced Multi poly- Bernoulli numbers and proved that special values of certain zeta functions at non-positive integers can be described in terms of these numbers. The study of Multi poly-Bernoulli and Euler numbers and their combinatorial relations has received much attention [2,4,6,7,12,13,14,19,22,27]. In this paper we introduce the generalization of Multi poly-Bernoulli and Euler numbers and consider some combinatorial relationships of the Generalized Multi poly-Bernoulli and Euler numbers of higher order. The present paper deals with Generalization of Multi poly-Bernouli numbers and polynomials of higher order. In 2002, Q. M. Luo and et al (see [11, 23, 24]) defined the generalization of Bernoulli polynomials and Euler numbers. Some earlier results of Luo in terms of generalized Multi poly-Bernoulli and Euler numbers, can be deduced. Also we investigate some relationships between Multi poly-Bernoulli and Euler polynomials.
- Subjects
EULER polynomials; ZETA functions; MATHEMATICAL sequences; BERNOULLI numbers; NUMERICAL analysis; MATHEMATICAL optimization
- Publication
International Journal of Mathematical Combinatorics, 2011, Vol 2, p117
- ISSN
1937-1055
- Publication type
Article