Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2017; 32(2): 305-319

Online first article April 17, 2017      Printed April 30, 2017

https://doi.org/10.4134/CKMS.c150228

Copyright © The Korean Mathematical Society.

Certain integral formulas associated with Aleph $(\aleph)$-function

Praveen Agarwal, Shilpi Jain, Erkinjon T. Karimov, and Jyotindra C. Prajapati

Anand International College of Engineering, Poornima College of Engineering, Academy of Sciences of the Republic of Uzbekistan, Marwadi Education Foundation Group of Institutions

Abstract

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Recently many authors have investigated so-called Aleph $(\aleph)$-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph $(\aleph)$-function. Precisely, integrals with product of Aleph $(\aleph)$-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.

Keywords: Aleph function, $I$-function, $H$-function, Jacobi polynomials, Legendre function, Bessel Maitland function, hypergeometric function

MSC numbers: 33C05, 33C20, 33C45, 33C60

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