Integral and computational representations of the extended Hurwitz–Lerch zeta function

Srivástava, H. M.; Pogány, Tibor K.; Saxena, R. K.

doi:10.1080/10652469.2010.530128

Cited by 92 publications

(78 citation statements)

References 16 publications

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“…Further studies of the Mittag-Leffler type functions can be found in the recent works by Gorenflo et al [5], Haubold et al [6], Kilbas et al [8,9], Kiryakova [11], Li et al [12], Saxena et al [16,17], Sharma et al [18][19][20], Srivastava et al [21,23,24,26], and Tomovski et al [27]. In particular, several interesting properties and characteristics of the Mittag-Leffer functions E α (z) and E α,β (z), as well as their known extensions and generalizations, were discussed by Saxena et al [17], Gorenflo et al [5], Srivastava et al [25,26], and Tomovski et al [27].…”

Section: Preliminariesmentioning

confidence: 99%

Generalized convolution properties based on the modified Mittag-Leffler function

Srivástava¹,

Kılıçman²,

Abdulnaby³

et al. 2017

J. Nonlinear Sci. Appl.

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Studies of convolution play an important role in Geometric Function Theory (GFT). Such studies attracted a large number of researchers in recent years. By making use of the Hadamard product (or convolution), several new and interesting subclasses of analytic and univalent functions have been introduced and investigated in the direction of well-known concepts such as the subordination and superordination inequalities, integral mean and partial sums, and so on. In this article, we apply the Hadamard product (or convolution) by utilizing some special functions. Our contribution in this paper includes defining a new linear operator in the form of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright p Ψ qfunction in the right-half of the open unit disk where where (z) > 0. We then show that the new linear convolution operator is bounded in some spaces. In particular, several boundedness properties of this linear convolution operator under mappings from a weighted Bloch space into a weighted-log Bloch space are also investigated. For uniformity and convenience, the Fox-Wright p Ψ q -notation is used in our results.

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Section: Preliminariesmentioning

confidence: 99%

Generalized convolution properties based on the modified Mittag-Leffler function

Srivástava¹,

Kılıçman²,

Abdulnaby³

et al. 2017

J. Nonlinear Sci. Appl.

Self Cite

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“…[3][4][5][6][7][8][9][10][11][12][13][14]. The present sequel to these earlier papers is motivated largely by the aforementioned works of Matsumoto and Kamano [15,16] In the present paper we introduce a new class of zeta functions ( )…”

Section: 7)mentioning

confidence: 99%

On Multiple Zeta Function and Associated Properties

Bin-Saad¹,

Pathan²,

Bin-Alhag³

2018

TJANT

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“…We denote by C the class of convex (univalent) functions in U and satisfying Recently, a new family of γ-generalized Hurwitz-Lerch zeta function was investigated by Srivastava [20] (see also [24,27] …”

Section: A[a J] = {F ∈ A(umentioning

confidence: 99%