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

Syed Ali Haider Shah; Shahid Mubeen; Syed Ali Haider Shah; Shahid Mubeen

doi:10.3934/math.2021676

AIMS Mathematics

2021, Volume 6, Issue 11: 11631-11641. doi: 10.3934/math.2021676

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

Syed Ali Haider Shah ^,,
Shahid Mubeen

Department of Mathematics, University of Sargodha, Sargodha, Pakistan

Received: 09 June 2021 Accepted: 05 August 2021 Published: 11 August 2021
MSC : 33C60, 33C10, 45P05

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.
- Meijer $ G $-function,
- generalized Meijer $ G $-function,
- Laguerre polynomial,
- hypergeometric function,
- confluent hypergeometric function
Citation: Syed Ali Haider Shah, Shahid Mubeen. Expressions of the Laguerre polynomial and some other special functions in terms of the generalized Meijer $ G $-functions[J]. AIMS Mathematics, 2021, 6(11): 11631-11641. doi: 10.3934/math.2021676

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Abstract

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.

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