Möbius inversion formulas related to the Fourier expansions of two-dimensional Apostol–Bernoulli polynomials

Bayad, Abdelmejid; Navas, Luis M.

doi:10.1016/j.jnt.2015.12.007

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“…It is worth mentioning that the Apostol-Bernoulli polynomials were firstly introduced by Apostol [6] (see also Srivastava [36] for a systematic study) in order to evaluate the value of the Hurwitz-Lerch zeta function. For some nice methods and results on these polynomials and numbers, one is referred to [7,8,26,32,33]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

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

He¹,

Kim²

2016

J. Nonlinear Sci. Appl.

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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.

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Section: Introductionmentioning

confidence: 99%

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

He¹,

Kim²

2016

J. Nonlinear Sci. Appl.

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Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials

Aracı

Srivástava

et al. 2018

Mathematics

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In this paper, we present a systematic and unified investigation for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. By applying the generating-function methods and summation-transform techniques, we establish some higher-order convolutions for the Apostol-Bernoulli polynomials, the Apostol-Euler polynomials and the Apostol-Genocchi polynomials. Some results presented here are the corresponding extensions of several known formulas.

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Möbius inversion formulas related to the Fourier expansions of two-dimensional Apostol–Bernoulli polynomials

Cited by 2 publications

References 14 publications

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

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

Higher-Order Convolutions for Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi Polynomials

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