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http://dx.doi.org/10.4134/CKMS.c210344

CERTAIN IMAGE FORMULAS OF (p, 𝜈)-EXTENDED GAUSS' HYPERGEOMETRIC FUNCTION AND RELATED JACOBI TRANSFORMS  

Chopra, Purnima (Marudhar Engineering College)
Gupta, Mamta (Amity School of Applied Sciences Amity University)
Modi, Kanak (Amity School of Applied Sciences Amity University)
Publication Information
Communications of the Korean Mathematical Society / v.37, no.4, 2022 , pp. 1055-1072 More about this Journal
Abstract
Our aim is to establish certain image formulas of the (p, 𝜈)-extended Gauss' hypergeometric function Fp,𝜈(a, b; c; z) by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erdélyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, 𝜈)-extended Gauss's hypergeometric function Fp,𝜈(a, b; c; z) and Fox-Wright function rΨs(z). We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the (p, 𝜈)-extended Gauss' hypergeometric function Fp,𝜈(a, b; c; z).
Keywords
$(p,{\nu})$-extended Gauss hypergeometric function $F_{p,{\nu}}(a,b; c; z)$; extended beta function; fractional calculus operators;
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