Generating functions for the generalized Gauss hypergeometric functions

Srivástava, H. M.; Agarwal, Praveen; Jain, Shilpi

doi:10.1016/j.amc.2014.08.105

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By Appealing B1

Upper Bounds1

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Cited by 51 publications

(49 citation statements)

References 15 publications

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“…Using the known formula (see [ [1]; p.182 (9) in the above expression and after some simplification, we get the desired result. (z), the following differential formula holds true:…”

mentioning

confidence: 91%

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A new generalization of confluent hypergeometric function and whittaker function

2018

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“…Using the known formula (see [ [1]; p.182 (9) in the above expression and after some simplification, we get the desired result. (z), the following differential formula holds true:…”

mentioning

confidence: 91%

“…Afterwards, Srivastava et al [9] introduced a new generalized Gauss hypergeometric functions as follows:…”

Section: By Appealing Bmentioning

confidence: 99%

A new generalization of confluent hypergeometric function and whittaker function

2018

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“…We need the following generalized hypergeometric functions in the sequel: Definition 2.1 Based on the generalized Beta function, the extended Gauss hypergeometric function is formulated by [5] …”

Section: Upper Boundsmentioning

confidence: 99%

Studies on Fractional Differential Operators of Two Parameters in a Complex Domain

Ibrahim¹,

Jalab²

2016

TJANT

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This study deals with a generalization for fractional differential operators in a complex domain based on the extended Beta function. Stipulations are imposed for these generalized operators such as the upper bounds. Other possessions for the above operator are also prepared. In addition, implementations of these operators are introduced and suggested in the geometric function theory (GFT). Sufficient conditions are imposed for functions to be univalent.

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“…In recent years, many authors considered the several extensions of well known special functions (see, for example, [2,3,9,12,13]; see also the very recent work [8,10]). In 1994, Chaudhry and Zubair [4], introduced the generalized representation of gamma function.…”

Section: Introductionmentioning

confidence: 99%

An extension of Caputo fractional derivative operator and its applications

Kıymaz¹,

Çetinkaya²,

Agarwa³

2016

J. Nonlinear Sci. Appl.

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In this paper, an extension of Caputo fractional derivative operator is introduced, and the extended fractional derivatives of some elementary functions are calculated. At the same time, extensions of some hypergeometric functions and their integral representations are presented by using the extended fractional derivative operator, linear and bilinear generating relations for extended hypergeometric functions are obtained, and Mellin transforms of some extended fractional derivatives are also determined.

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Generating functions for the generalized Gauss hypergeometric functions

Cited by 51 publications

References 15 publications

A new generalization of confluent hypergeometric function and whittaker function

A new generalization of confluent hypergeometric function and whittaker function

Studies on Fractional Differential Operators of Two Parameters in a Complex Domain

An extension of Caputo fractional derivative operator and its applications

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