Extended hypergeometric and confluent hypergeometric functions

Chaudhry, M. Aslam; Qadir, Asghar; Srivástava, H. M.; Paris, R. B.

doi:10.1016/j.amc.2003.09.017

Cited by 180 publications

(199 citation statements)

References 5 publications

Supporting

Mentioning

196

Contrasting

Order By: Relevance

“…Changing a, b and c to a + 1, b + 1 and c + 1 in (6.4), respectively, Now for m = 1, (11.3) leads to Chaudhry et al [6] and for p = 0, (11.3) reduces to Gauss's summation formula (11.1).…”

Section: Recurrence Relations For the Geghf And Gechfmentioning

confidence: 99%

“…Clearly when m = 1 in (7.4) and (7.5) leads to the differentiation formulas for Chaudhry et al [6] and for p = 0 in (7.4) and (7.5) lead to the differential formulas for usual GHF and CHF [10].…”

Section: Differentiation Formulas For the Geghf And Gechfmentioning

confidence: 99%

“…Thus we have Clearly for m = 1 in (6.4) -(6.9) leads to the integral representation of Chaudhry et al [6] and for p = 0 in (6.4) -(6.9) leads to integral representation of the usual GHF and CHF [10, pp. 20-23].…”

Section: Integral Representations Of the Generalized Hypergeometric Amentioning

confidence: 99%

“…, where e(c) > e(b) > 0. In recent years, several extensions of the wellknown special functions have been considered by some authors [1][2][3][4][5][6][7]. In 1994, Chaudhry and Zubair [1] have introduced the following extension of gamma function…”

Section: Introductionmentioning

confidence: 99%

“…It is clearly seen that when p = 0, (1.7) and (1.8) reduces to original gamma function and beta function. Recently, Chaudhry et al [6] used B(x, y; p) to extend the hypergeometric functions and confluent hypergeometric functions as follows;…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Generalization of Extended Beta Function, Hypergeometric and Confluent Hypergeometric Functions

Lee¹,

Rathie²,

Parmar³

et al. 2011

Honam Mathematical Journal

View full text Add to dashboard Cite

Abstract. The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas, transform formulas, recurrence relations, summation formula for these new generalization.

show abstract

“…Changing a, b and c to a + 1, b + 1 and c + 1 in (6.4), respectively, Now for m = 1, (11.3) leads to Chaudhry et al [6] and for p = 0, (11.3) reduces to Gauss's summation formula (11.1).…”

Section: Recurrence Relations For the Geghf And Gechfmentioning

confidence: 99%

Section: Differentiation Formulas For the Geghf And Gechfmentioning

confidence: 99%

Section: Integral Representations Of the Generalized Hypergeometric Amentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Generalization of Extended Beta Function, Hypergeometric and Confluent Hypergeometric Functions

Lee¹,

Rathie²,

Parmar³

et al. 2011

Honam Mathematical Journal

View full text Add to dashboard Cite

show abstract

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

Srivástava

Agarwal

Jain

2016

Math Methods in App Sciences

View full text Add to dashboard Cite

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.

show abstract