Some properties of a family of incomplete hypergeometric functions

Srivastava, Rekha

doi:10.1134/s1061920813010111

Cited by 34 publications

(24 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For x = 0, the generating functions (43) to (48) were given by Chaundy [11] who also gave a much more general result than the case of the generating functions (49) and (50) when x = 0 (see, for details, [42,Section 2.6]; see also [33]). In fact, as already observed by Srivastava [33, p. 329], the case of the generating functions (49) and (50) when x = 0 (see [33, p. 329 …”

Section: Remark 4 the Generating Functionsmentioning

confidence: 99%

“…(49) and (50) are the limit cases of the generating functions (43) and (44), respectively, if we first replace t in (43) and (44) by t/λ and then proceed to the limit when |λ | → ∞. Furthermore, the generating functions (49) and (50) can be deduced also as the limit cases of the generating functions (47) and (48), respectively, if we first replace t and z in (47) and (48) by t/λ and λ z, respectively, and then proceed to the limit when |λ | → ∞.…”

Section: Remarkmentioning

confidence: 99%

See 1 more Smart Citation

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

Srivastava¹

2013

Appl. Math. Inf. Sci.

View full text Add to dashboard Cite

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.

show abstract

Section: Remark 4 the Generating Functionsmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

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

Srivastava¹

2013

Appl. Math. Inf. Sci.

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

“…It is noted that both γ(s, x) and Γ(s, x) which are given in (2.12) and (2.13), respectively, are certain generalizations of the classical Gamma function Γ(z) and have proved to be important for physicists and engineers as well as mathematicians. For more details, one may refer to the following literature: [1], [14], [15], [27], [50], [51], [52], [53], [54], [60] and [62].…”

Section: Generalized Special Functionsmentioning

confidence: 99%

Fractional Calculus Operators and Their Image Formulas

Agarwal¹,

Choi²

2016

Journal of the Korean Mathematical Society

View full text Add to dashboard Cite

Abstract. During the past four decades or so, due mainly to a wide range of applications from natural sciences to social sciences, the so-called fractional calculus has attracted an enormous attention of a large number of researchers. Many fractional calculus operators, especially, involving various special functions, have been extensively investigated and widely applied. Here, in this paper, in a systematic manner, we aim to establish certain image formulas of various fractional integral operators involving diverse types of generalized hypergeometric functions, which are mainly expressed in terms of Hadamard product. Some interesting special cases of our main results are also considered and relevant connections of some results presented here with those earlier ones are also pointed out.

show abstract

Some properties of a family of incomplete hypergeometric functions

Cited by 34 publications

References 14 publications

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

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

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

Fractional Calculus Operators and Their Image Formulas

Contact Info

Product

Resources

About