Generating functions for a certain class of incomplete hypergeometric polynomials

Srivastava, Rekha; Cho, Nak Eun

doi:10.1016/j.amc.2012.09.059

Cited by 36 publications

(31 citation statements)

References 12 publications

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“…The currently popular literature on Special Functions contains several generalizations of the Gamma function .z/, the Beta function B.˛,ˇ/, the hypergeometric functions 1 F 1 and 2 F 1 , and the generalized hypergeometric functions r F s with r numerator and s denominator parameters (see, for details, [1,2,[8][9][10][11][12][13][14][15][16][17][18][19][20][21] and the references cited in each of these papers). In particular, for an appropriately bounded sequence fÄ`g`2 N0 of essentially arbitrary (real or complex) numbers, Srivastava et al [16, p. 243, Eq.…”

Section: Introduction Definitions and Preliminariesmentioning

confidence: 99%

Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributions

Srivástava

Agarwal

Jain

2016

Math. Meth. Appl. Sci.

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In the present paper, our aim is to establish several formulas involving integral transforms, fractional derivatives, and a certain family of extended generalized hypergeometric functions. As corollaries and consequences, many interesting results are shown to follow from our main results. A probability density function involving the extended generalized hypergeometric function is introduced, and its properties are studied. The corresponding properties of some of the classical probability distributions and their associated probability density functions are easily derivable as special cases of our general results. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Introduction Definitions and Preliminariesmentioning

confidence: 99%

Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributions

Srivástava

Agarwal

Jain

2016

Math. Meth. Appl. Sci.

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“…Some interesting special cases of our main results are also pointed out. For various other investigations involving generalizations of the hypergeometric function p F q of p numerator and q denominator parameters, which were motivated essentially by the pioneering work of Srivastava et al [28], the interested reader may be referred to several recent papers on the subject (see, e.g., [6,8,9,16,27,33,35,36,37,38,39] and the references cited in each of these papers).…”

Section: Throughout This Paper N Zmentioning

confidence: 99%

The INCOMPLETE GENERALIZED Τ-Hypergeometric AND SECOND Τ-Appell FUNCTIONS

Parmar¹,

Saxena²

2016

Journal of the Korean Mathematical Society

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Abstract. Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] and the second Appell function [Appl. Math. Comput. 219 (2013), 8332-8337] by means of the incomplete Pochhammer symbols (λ; κ) ν and [λ; κ] ν , we introduce here the family of the incomplete generalized τ -hypergeometric functions 2 γ τ 1 (z) and 2 Γ τ 1 (z). The main object of this paper is to study these extensions and investigate their several properties including, for example, their integral representations, derivative formulas, Euler-Beta transform and associated with certain fractional calculus operators. Further, we introduce and investigate the family of incomplete second τ -Appell hypergeometric functions Γ τ 1 ,τ 2 2 and γ τ 1 ,τ 2 2 of two variables. Relevant connections of certain special cases of the main results presented here with some known identities are also pointed out.

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“…The main generating functions for the aforementioned associated class of generalized incomplete hypergeometric polynomials are contained in the following theorem (see also [50]). …”

Section: Generating Functions Based Upon the Lagrange Expansion Theormentioning

confidence: 99%

Some Generalizations of Pochhammer’s Symbol and their Associated Families of Hypergeometric Functions and Hypergeometric Polynomials

Srivastava¹

2013

Appl. Math. Inf. Sci.

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Abstract:In 2012, H. M. Srivastava et al. [37] introduced and studied a number of interesting fundamental properties and characteristics of a family of potentially useful incomplete hypergeometric functions. The definitions of these incomplete hypergeometric functions were based essentially upon some generalization of the Pochhammer symbol by mean of the incomplete gamma functions γ(s, x) and Γ (s, x). Our principal objective in this article is to present a systematic investigation of several further properties of these incomplete hypergeometric functions and some general classes of the incomplete hypergeometric polynomials which are associated with them. Various (known or new) special cases and consequences of the results presented in this article are considered. Several other generalizations of the Pochhammer symbol and their associated families of hypergeometric functions and hypergeometric polynomials are also briefly pointed out.

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Generating functions for a certain class of incomplete hypergeometric polynomials

Cited by 36 publications

References 12 publications

Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributions

Integral transform and fractional derivative formulas involving the extended generalized hypergeometric functions and probability distributions

The INCOMPLETE GENERALIZED Τ-Hypergeometric AND SECOND Τ-Appell FUNCTIONS

Some Generalizations of Pochhammer’s Symbol and their Associated Families of Hypergeometric Functions and Hypergeometric Polynomials

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