Extension of Euler's beta function

Chaudhry, Muhammad Anwar; Qadir, Asghar; Rafique, M. Mujahid; Zubair, Syed M.

doi:10.1016/s0377-0427(96)00102-1

Cited by 233 publications

(198 citation statements)

References 4 publications

Supporting

Mentioning

195

Contrasting

Order By: Relevance

“…, 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%

See 1 more Smart Citation

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

Section: Introductionmentioning

confidence: 99%

“…Clearly when m = 1, equation (1.13) reduces to Chaudhry et al [2] extended beta function (EBF) and p = 0, it reduces to usual Euler's beta function [9].…”

Section: Introductionmentioning

confidence: 99%

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

“…Extensions of a number of well-known special functions were investigated recently by several authors (see [7]- [9], [24]). In particular, Chaudhry et al [7, p. 20 In 2004, Chaudhry et al [8] used B(x, y ; p) to extend the hypergeometric and the confluent hypergeometric functions as follows:…”

Section: Introductionmentioning

confidence: 99%

Some generating functions and properties of extended second Appell function

Parmar¹,

Purohıt

2017

B Soc Paran Mat

View full text Add to dashboard Cite

Various families of generating functions have been established by a number of authors in many different ways. In this paper, we aim at establishing (presumably new) a generating function for the extended second Appell hypergeometric function F 2 (a, b, b ′ ; c, c ′ ; x, y; p). Further we derive a relation in terms of the Laguerre polynomials and differentiation formulas. We also present special cases of the main results of this paper.

show abstract

“…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%

“…In 1994, Chaudhry and Zubair [4], introduced the generalized representation of gamma function. In 1997, Chaudhry et al [2] presented the following extension of Euler's beta function …”

Section: Introductionmentioning

confidence: 99%

An extension of Caputo fractional derivative operator and its applications

Kıymaz¹,

Çetinkaya²,

Agarwa³

2016

J. Nonlinear Sci. Appl.

View full text Add to dashboard Cite

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.

show abstract

Extension of Euler's beta function

Cited by 233 publications

References 4 publications

Generalization of Extended Beta Function, Hypergeometric and Confluent Hypergeometric Functions

Generalization of Extended Beta Function, Hypergeometric and Confluent Hypergeometric Functions

Some generating functions and properties of extended second Appell function

An extension of Caputo fractional derivative operator and its applications

Contact Info

Product

Resources

About