Explicit Formulas Associated with Some Families of Generalized Bernoulli and Euler Polynomials

Boutiche, Mohamed Amine; Rahmani, Mourad; Srivástava, H. M.

doi:10.1007/s00009-017-0891-0

Cited by 17 publications

(18 citation statements)

References 9 publications

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“…The numbers (b n (m)) n≥0 defined in (47) are called Daehee numbers of the first kind of order m by Kim et al [14]. A similar result to that in Theorem 5 can be found in the recent paper by Boutiche et al [6].…”

Section: Generalized Bernoulli Polynomials Of Real Ordermentioning

confidence: 56%

“…and show that the generalized Bernoulli and Euler polynomials of complex order can be written in terms of such numbers. In this respect, our results in Section 5, particularly Theorem 2, appear as generalizations of the results in [6]. Of course, the main problem is to give an explicit expression of the sequence a = (a n ) n≥0 as simple as possible.…”

Section: Introductionmentioning

confidence: 74%

“…We mention that Theorem 7 has recently been obtained by Boutiche et al [6] for the generalized Euler polynomials E(t, 1/2; x) by using the generalized Stirling numbers S k n (x) defined in (3).…”

Section: ⊓ ⊔mentioning

confidence: 94%

“…This is done in section 5. In a recent paper, Boutiche et al [6] define the generalized Stirling numbers S k n (x) as S k n (x) = ∆ k I n (x) k! , n, k = 0, 1, .…”

Section: Introductionmentioning

confidence: 99%

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Closed form expressions for Appell polynomials

Adell

Lekuona

2018

Ramanujan J

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We show that any Appell sequence can be written in closed form as a forward difference transformation of the identity. Such transformations are actually multipliers in the abelian group of the Appell polynomials endowed with the operation of binomial convolution. As a consequence, we obtain explicit expressions for higher order convolution identities referring to various kinds of Appell polynomials in terms of the Stirling numbers. Applications of the preceding results to generalized Bernoulli and Apostol-Euler polynomials of real order are discussed in detail.

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Section: Generalized Bernoulli Polynomials Of Real Ordermentioning

confidence: 56%

Section: Introductionmentioning

confidence: 74%

Section: ⊓ ⊔mentioning

confidence: 94%

“…This is done in section 5. In a recent paper, Boutiche et al [6] define the generalized Stirling numbers S k n (x) as S k n (x) = ∆ k I n (x) k! , n, k = 0, 1, .…”

Section: Introductionmentioning

confidence: 99%

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Closed form expressions for Appell polynomials

Adell

Lekuona

2018

Ramanujan J

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“…In particular, for m = 1, we get Relation (3.3) given in [6], and setting x = r for a fixed m in (11), we get…”

Section: Explicit Formulas For the Generalized Euler Polynomialsmentioning

confidence: 99%

Some explicit formulas for the generalized Frobenius-Euler polynomials of higher order

Belbachir¹,

Souddi²

2019

Filomat

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Our aim is to derive some explicit formulas for the generalized Bernoulli and Euler polynomials in terms of Whitney and translated Whitney numbers of the second kind. Also we derive some explicit formulas for the generalized Euler polynomials and Genocchi-like polynomials in terms of generalized Whitney polynomials of the second kind. We provide an algorithm for computing the generalized Frobenius-Euler polynomials of higher order.

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