( ISSN 2277 - 9809 (online) ISSN 2348 - 9359 (Print) ) New DOI : 10.32804/IRJMSH

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APOSTOL-BERNOULLI POLYNOMIAL AND THEIR PROPERTIES

    1 Author(s):  DR. RAM PRASAD DANGI

Vol -  10, Issue- 4 ,         Page(s) : 73 - 76  (2019 ) DOI : https://doi.org/10.32804/IRJMSH

Abstract

The Apostol Bernoulli polynomials are natural generalization of Bernoulli polynomials, they were first introduced by Apostol [1],[3] in order to study the Lipschitz - Lerch zeta functions. This paper is devoted to derive the recurrence relation and investigate some interesting properties of the Apostol Bernoulli polynomials.

[1] Boyadzhiev,khristo N., “Apostol-Bernoulli functions,derivative  polynimials and  Eulerrian    polynomials”, ArLXiv: 0710.1124.
[2] Ding, D., and Yang, J., (2010),“Some identities related to the Apostol Euler and Apostol Bernoulli polynomials”, advanced studies in contemporary mathematics, Vol. 20, No.1, pp. 7-21.
[3]Garg, M., Jain, K., and Srivastava, H.M., (2006),“some relation between the generalized Apostol-Bernoulli polynomials and Hurwitz-Lerch Zeta function”, Intergal transforms Spec. Funct., 17, pp. 803-815.
 [4] Zhang, Z.-Z, and Yang, H.-Q., (2008),“Several identities for the generalized Apostol-Bernoulli polynomials”, Comput. Math. Appl., 56. pp. 2993-2999.

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