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A note on Wright-type generalized $q$-hypergeometric function
The Bulletin of Irkutsk State University. Series Mathematics, Tome 48 (2024), pp. 80-94 Cet article a éte moissonné depuis la source Math-Net.Ru

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In 2001, Virchenko et al. published a paper on a new generalization of Gauss hypergeometric function, namely Wright-type generalized hypergeometric function. Present work aims to define the $q$-analogue generalized hypergeometric function, which reduces to generalized hypegeometric function by letting q tends to one, and study some new properties. Convergence of the series defining generalized $q$-hypergeometric function and properties including certain differentiation formulae and integral representations have been deduced.
Keywords: basic hypergeometric functions in one variable ${}_r \phi_s$, $q$-gamma functions, $q$-beta functions and integrals, $q$-calculus and related topics. 
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Kuldipkumar K. Chaudhary; Snehal B. Rao. A note on Wright-type generalized $q$-hypergeometric function. The Bulletin of Irkutsk State University. Series Mathematics, Tome 48 (2024), pp. 80-94. http://geodesic.mathdoc.fr/item/IIGUM_2024_48_a5/

[1] Al-Omari S., Kilicman A., Notes on the q-Analogues of the Natural Transforms and Some Further Applications, 2015, arXiv: 1510.00406

[2] Andrews G., q-Series: Their development and application in analysis, number theory, combinatorics, physics, and computer algebra, American Mathematical Soc., 1986 | MR | Zbl

[3] Bhardwaj H., Sharma P., “An Application of q-Hypergeometric Series”, GANITA, 71:1 (2021), 161–169 | MR | Zbl

[4] Ciavarella A., What is q-Calculus, v. 1, Course Hero, 2016

[5] Charalambides C.A., “Review of the basic discrete q-distributions”, Lattice Path Combinatorics And Applications, 58 (2019), 166–193 | DOI | MR | Zbl

[6] Ernst T., “A method for q-calculus”, Journal Of Nonlinear Mathematical Physics, 10:4 (2003), 487–525 | DOI | MR | Zbl

[7] Gasper G., Rahman M., Basic hypergeometric series, Cambridge univ. press, 2004 | MR | Zbl

[8] Gauss C.F., Disquistiones Generales circa Seriem Infinitam 1+ $\alpha$$\beta$/1. $\gamma$x+ $\alpha$ ($\alpha$+ 1) $\beta$ ($\beta$+ 1)/1.2. $\gamma$ ($\gamma$+ 1) xx+ $\alpha$ ($\alpha$+ 1)($\alpha$+ 2) $\beta$ ($\beta$+ 1)($\beta$+ 2)/1.2. 3. $\gamma$ ($\gamma$+ 1)($\gamma$+ 2) x\^ 3+ etc., Thesis, Gottingen, 1866

[9] Mansour M., “An asymptotic expansion of the q-gamma function $\Gamma _ q (x)$”, Journal Of Nonlinear Mathematical Physics, 13:4 (2006), 479–483 | DOI | MR | Zbl

[10] Mathai A., Haubold H., Special functions for applied scientists, Springer, 2008 | Zbl

[11] Rainville E.D., Special Functions, Macmillan, 1960 | MR | Zbl

[12] Rao S.B., Prajapati J.C., Shukla A.K., “Wright type hypergeometric function and its properties”, Adv. Pure Math., 3:3 (2013), 335–342 | DOI

[13] Rao S.B., Shukla A.K., “Note on generalized hypergeometric function”, Integral Transforms And Special Functions, 24:11 (2013), 896–904 | DOI | MR | Zbl

[14] Virchenko N., Kalla S., Al-Zamel A., “Some results on a generalized hypergeometric function”, Integral Transforms And Special Functions, 12:1 (2001), 89–100 | DOI | MR | Zbl

[15] Wallis J., Arithmetica infinitorum, 1655