On hypergeometric functions and Pochhammer -symbol.

By Rafael Díaz, Eddy Pariguan. 2004

494 citations recorded by the source corpus.

We introduce the k-generalized gamma function ik, beta function Bk and Pochhammer k-symbol (x)n;k. We prove several identities generalizing those satisfled by the classical gamma function, beta function and Pochhammer symbol. We provide integral representation for the ik and Bk functions.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/36da455c5679166a8e1158aa04aca17a945242e1

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

On the k-Riemann-Liouville Fractional Derivative (2013, methodology): “The main object of this paper is to introduce a new fractional operator called k-Riemann-Liouville fractional derivative defined by using the k-Gamma function, which is a generalization of the classical Gamma function.”
(k, s)-Riemann-Liouville fractional integral and applications (2016, background): “Recently, in [6], Diaz and Pariguan have defined new functions called k-gamma and k-beta functions and the Pochhammer k-symbol that is respectively generalization of the classical gamma and beta functions and the classical Pochhammer symbol: Γk(x) = lim n→∞ n!k(nk) x k−1 (x)n,k , k > 0, where (x)n,k”
Properties and Inequalities of Generalized k-Gamma, Beta and Zeta Functions (2010, background): “1 Introduction In [2] the authors introduced the generalized k-Gamma function Γk(x) as Γk(x) = lim n→∞ n!kn(nk)x/k−1 (x)n,k , k > 0, x ∈ C − kZ−, (1.”
Some inequalities involving Hadamard‐type k‐fractional integral operators (2017, background): “3 Let k > 0, then the generalized k gamma function is defined by [18]: k.”
Generation of new fractional inequalities via n polynomials s-type convexity with applications (2020, unknown): “where ΓK(α) is the K-Gamma function [71] defined by ΓK(α) = ∫ ∞”
On Pólya–Szegö and Čebyšev type inequalities via generalized k-fractional integrals (2020, unknown): “respectively, where Γk( ) = ∫ ∞ 0 t –1e– tk k dt is the k-gamma function [89].”
On generalized fractional integral inequalities for the monotone weighted Chebyshev functionals (2020, unknown): “where Γκ is the κ-gamma function defined in [15].”
On the k-Riemann-Liouville fractional integral and applications (2014, background): “Recently, Diaz and Pariguan (2007) have defined new functions calledk -gamma andk -beta functions and the Pochhammer k -symbol that is generalization of the classical gamma and beta functions and the classical Pochhammer symbol.”
k -Fractional Integrals and Application (2012, methodology): “(6) Following Diaz [2], we define k -hypergeometric function kF by the series ( ) ( )( ), ; , ;kF k k xβ γ = ( )( ) , 0 , ! j j k j j k x j β γ ∞ = ∑ .”