Expressions of the Laguerre polynomial and some other special functions in terms of the generalized Meijer $ G $-functions

Abstract

<abstract><p>In this paper, we investigate the relation of generalized Meijer $ G $-functions with some other special functions. We prove the generalized form of Laguerre polynomials, product of Laguerre polynomials with exponential functions, logarithmic functions in terms of generalized Meijer $ G $-functions. The generalized confluent hypergeometric functions and generalized tricomi confluent hypergeometric functions are also expressed in terms of the generalized Meijer $ G $-functions.</p></abstract>

Certain Integral and Differential Formulas Involving the Product of Srivastava’s Polynomials and Extended Wright Function

“…Following are the special cases of results discussed above. (i) The formulas obtained reduce to formulas for Saigo's fractional differential operators (18) and (19) for ξ = 0; (ii) By substituting η = −ξ in Saigo's fractional differential operators, we obtain the formulas for Riemann-Liouville fractional differential operators (22) and (23).…”

“…Fractional calculus and integral transforms of general class of polynomials and incomplete Fox-Wright functions is discussed by Jangid et al [21]. Certain expressions of the Laguerre polynomial and relations of some known functions in terms of generalized Meijer G-functions are explored in [22,23].…”