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arXiv · 2104.09143

On extension of the $_{r}R_{s,q}(\alpha,\beta,z)$ function and their $q$-calculus

Ayman Shehata·Dinesh Kumar
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Abstract

In this article, we investigate and establish some properties including analytic properties, contiguous relations, differential properties, differential operators, an expansion formula, and simple integrals, integral operators, some fractional integral properties, some new integral representations, the Riemann Liouville fractional $q$-derivative and $q$-integral operators of $q$-analogue of various basic $_{r}R_{s,q}$ function by using technique of $q$-calculus. Certain interesting consequences of the theorem are also discussed by considering some examples.

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Ayman Shehata, Dinesh Kumar. 2021-04-19. On extension of the $_{r}R_{s,q}(\alpha,\beta,z)$ function and their $q$-calculus. https://arxiv.org/abs/2104.09143

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