Padé approximation and Apostol–Bernoulli and Apostol–Euler polynomials

Prévost, Marc

doi:10.1016/j.cam.2009.11.050

Cited by 22 publications

(11 citation statements)

References 19 publications

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“…The popularity of Hermite, Bernoulli and Euler polynomials in number theory, combinatorics and mathematical physics is due in part to the papers of researchers in [3] to [5], [9] to [14], [18], [19], [20], [22] and their generalizations and various extensions which appeared in the literature. In this paper, we propose a further generalization of Apostol-Euler polynomials and Apostol-Genocchi polynomials and we give some properties involving them.…”

Section: Respectivelymentioning

confidence: 99%

Some New Classes of Generalized Hermite-Based Apostol-Euler and Apostol-Genocchi Polynomials

Pathan¹,

Khan

2015

Fasciculi Mathematici

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Section: Respectivelymentioning

confidence: 99%

Some New Classes of Generalized Hermite-Based Apostol-Euler and Apostol-Genocchi Polynomials

Pathan¹,

Khan

2015

Fasciculi Mathematici

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“…For some elegant results and nice methods on these polynomials and numbers, we refer the reader to [9,19,21,23,26]. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 99%

Some new results on products of Apostol–Bernoulli and Apostol–Euler polynomials

2015

Journal of Mathematical Analysis and Applications

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We perform a further investigation for the Apostol-Bernoulli and Apostol-Euler polynomials and numbers. By making use of an elementary idea used by Euler in the discovery of his famous Pentagonal Number Theorem, we establish some new formulae for products of an arbitrary number of Apostol-Bernoulli and ApostolEuler polynomials and numbers. These results are the corresponding generalizations of some known formulae including the higher-order convolution ones discovered by Agoh and Dilcher (2014) [5] on the classical Bernoulli and Euler polynomials.

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“…In 2006, Luo [10] invented the generalized Apostol-Euler polynomials E (α) n (x; λ) of order α ∈ C. Many authors have investigated these polynomials and numerous very interesting papers can be found in the literature. The reader should read [11][12][13][14][15][16][17][18][19][20].…”

Section: Introductionmentioning

confidence: 99%

A new class of generalized Apostol–Bernoulli polynomials and some analogues of the Srivastava–Pintér addition theorem

Tremblay

Gaboury

Fugère

2011

Applied Mathematics Letters

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a b s t r a c tThe main purpose of this paper is to introduce and investigate a new class of generalized Apostol-Bernoulli polynomials based on a definition given by Natalini and Bernardini (2003) [22] for the generalized Bernoulli polynomials. We obtain a generalization of the Srivastava-Pintér addition theorem (Srivastava and Pintér (2004) [23]). We also give a list of expressions involving special functions that could be used to obtain some analogues of the Srivastava-Pintér addition theorem. Finally, we give an analogue featuring the new class of generalized Apostol-Bernoulli polynomials.

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Padé approximation and Apostol–Bernoulli and Apostol–Euler polynomials

Cited by 22 publications

References 19 publications

Some New Classes of Generalized Hermite-Based Apostol-Euler and Apostol-Genocchi Polynomials

Some New Classes of Generalized Hermite-Based Apostol-Euler and Apostol-Genocchi Polynomials

Some new results on products of Apostol–Bernoulli and Apostol–Euler polynomials

A new class of generalized Apostol–Bernoulli polynomials and some analogues of the Srivastava–Pintér addition theorem

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