Some generalizations of the Apostol–Genocchi polynomials and the Stirling numbers of the second kind

Luo, Qiu-Ming; Srivástava, H. M.

doi:10.1016/j.amc.2010.12.048

Cited by 147 publications

(151 citation statements)

References 30 publications

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“…With a view to use it in deriving our first set of addition formulas for the Appell polynomials {f n (x)} n∈N0 given by (9) and (10), we present the following lemma.…”

Section: The First Set Of Addition Formulasmentioning

confidence: 99%

“…I, p. 35 et seq.] and [11]; see also [6,8,9] and the references cited therein). Recently, Chen et al [4] presented several general classes of multiplication formulas and polynomial expansions in series of the Bernoulli and Euler polynomials for the Srivastava polynomials S N n (x) which are defined, in terms of a suitably bounded double sequence {A m,n } m,n∈N0 of essentially arbitrary (real or complex) parameters, by (cf.…”

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confidence: 99%

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Addition theorems for the Appell polynomials and the associated classes of polynomial expansions

Pintér

Srivástava

2012

Aequat. Math.

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n (x) and the generalized Euler polynomials E (α) n (x) of order α and degree n in x. The main purpose of this sequel to some of the aforecited investigations is to give several addition formulas for a general class of Appell sequences. The addition formulas, which are derived in this paper, involve not only the generalized Bernoulli polynomials B (α) n (x) and the generalized Euler polynomials E (α) n (x), but also the generalized Genocchi polynomials G (α) n (x), the Srivastava polynomials S N n (x), several general families of hypergeometric polynomials and such orthogonal polynomials as the Jacobi, Laguerre and Hermite polynomials. Some umbral-calculus generalizations of the addition formulas are also investigated.Mathematics Subject Classification (2010). Primary 11B68; Secondary 11B83, 33C45.

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“…With a view to use it in deriving our first set of addition formulas for the Appell polynomials {f n (x)} n∈N0 given by (9) and (10), we present the following lemma.…”

Section: The First Set Of Addition Formulasmentioning

confidence: 99%

mentioning

confidence: 99%

Addition theorems for the Appell polynomials and the associated classes of polynomial expansions

Pintér

Srivástava

2012

Aequat. Math.

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“…These numbers occur in combinatorics and in the theory of partitions (cf. [31], [16], [33]). In [31], we constructed a new generating function, related to nonnegative real parameters, for the generalized  -Stirling type numbers of the second kind.…”

Section: Generating Functionsmentioning

confidence: 99%

Identities Associated with Generalized Stirling Type Numbers and Eulerian Type Polynomials

Şimşek

2013

MCA

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Abstract-By using the generating functions for the generalized Stirling type numbers, Eulerian type polynomials and numbers of higher order, we derive various functional equations and differential equations. By using these equation, we derive some relations and identities related to these numbers and polynomials. Furthermore, by applying padic Volkenborn integral to these polynomials, we also derive some new identities for the generalized  -Stirling type numbers of the second kind, the generalized array type polynomials and the generalized Eulerian type polynomials.

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“…(see for detail [4], [6], [9], [10], [13]- [19], [21], [24], [30] see also the references cited in each of these earlier works).…”

Section: Introductionmentioning

confidence: 99%

A New Class of Laguerre-based Generalized Apostol Polynomials

Khan¹,

Usman²

2016

Fasciculi Mathematici

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Some generalizations of the Apostol–Genocchi polynomials and the Stirling numbers of the second kind

Cited by 147 publications

References 30 publications

Addition theorems for the Appell polynomials and the associated classes of polynomial expansions

Addition theorems for the Appell polynomials and the associated classes of polynomial expansions

Identities Associated with Generalized Stirling Type Numbers and Eulerian Type Polynomials

A New Class of Laguerre-based Generalized Apostol Polynomials

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