Apostol-Euler Polynomials of Higher Order and Gaussian Hypergeometric Functions

Luo, Qiu-Ming

doi:10.11650/twjm/1500403883

Cited by 125 publications

(77 citation statements)

References 6 publications

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“…Luo and Srivastava [10,11,12] introduced the generalized Apostol-Bernoulli polynomials B (α) n (x) of order α, Luo [7] investigated the generalized Apostol-Euler polynomials E (α) n (x) of order α and the generalized Apostol-Genocchi polynomials G (α) n (x) of order α (see also [6,8,9]). …”

Section: })mentioning

confidence: 99%

Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials

Khan¹,

Nisar²

2018

Preprint

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Abstract. In this paper, we introduce a general family of Lagrange-based Apostoltype Hermite polynomials thereby unifying the Lagrange-based Apostol HermiteBernoulli and the Lagrange-based Apostol Hermite-Genocchi polynomials. We also define Lagrange-based Apostol Hermite-Euler polynomials via the generating function. In terms of these generalizations, we find new and useful relations between the unified family and the Apostol Hermite-Euler polynomials. We also derive their explicit representations and list some basic properties of each of them. Some implicit summation formulae and general symmetry identities are derived by using different analytical means and applying generating functions.

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confidence: 99%

Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials

Khan¹,

Nisar²

2018

Preprint

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“…where B (α) n (x) denotes the well-known and largely investigated generalized Bernoulli polynomials [7,11,12,13,14,15,26,28,29,31,37].…”

Section: Applications To Generalized Degenerate Bernoulli Polynomialsmentioning

confidence: 99%

A Further Investigation of Generating Functions Related to Pairs of Inverse Functions With Applications to Generalized Degenerate Bernoulli Polynomials

Gaboury¹,

Tremblay²

2014

Bulletin of the Korean Mathematical Society

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“…All authors are partially supported by Research Project Offices Akdeniz Universities. The author would like to thank to all referees for their valuable comments and also for suggesting references [7][8][9][10][11][12][13][14]. …”

Section: Acknowledgementsmentioning

confidence: 99%

Generating function for q-Eulerian polynomials and their decomposition and applications

Alkan

Şimşek

2013

Fixed Point Theory Appl

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The aim of this paper is to define a generating function for q-Eulerian polynomials and numbers attached to any character χ of the finite cyclic group G. We derive many functional equations, q-difference equations and partial deferential equations related to these generating functions. By using these equations, we find many properties of q-Eulerian polynomials and numbers. Using the generating element of the finite cyclic group G and the generating element of the subgroups of G, we show that the generating function with a conductor f can be written as a sum of the generating function with conductors which are less than f . MSC: 05A40; 11B83; 11B68; 11S80

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Apostol-Euler Polynomials of Higher Order and Gaussian Hypergeometric Functions

Cited by 125 publications

References 6 publications

Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials

Some New Classes of Generalized Lagrange-Based Apostol Type Hermite Polynomials

A Further Investigation of Generating Functions Related to Pairs of Inverse Functions With Applications to Generalized Degenerate Bernoulli Polynomials

Generating function for q-Eulerian polynomials and their decomposition and applications

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