General convolution identities for Apostol-Bernoulli, Euler and Genocchi polynomials

Volume 9, Issue 6, pp 4780--4797 http://dx.doi.org/10.22436/jnsa.009.06.115

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Authors

Yuan He - Faculty of Science, Kunming University of Science and Technology, 650500 Kunming, Yunnan, P. R. China. Taekyun Kim - Department of Mathematics, Kwangwoon University, Seoul 139-701, Korea.

Abstract

We perform a further investigation for the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. By making use of the generating function methods and summation transform techniques, we establish some general convolution identities for the Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials. These results are the corresponding extensions of some known formulas including the general convolution identities discovered by Dilcher and Vignat [K. Dilcher, C. Vignat, J. Math. Anal. Appl., 435 (2016), 1478-1498] on the classical Bernoulli and Euler polynomials.

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Keywords

• Apostol-Bernoulli polynomials and numbers
• Apostol-Euler polynomials and numbers
• Apostol-Genocchi polynomials and numbers
• combinatorial identities.

MSC

•  11B68
•  05A19

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