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2023•Asian-European Journal of MathematicsRequires access

Solution of conformable Laguerre and associated Laguerre equations using Laplace transform

Eqab M. Rabei, A. Al-Jamel, Mohamed Ghaleb Al-Masaeed

Open publisher page 4 citations

Abstract

In this paper, the conformable Laguerre and associated Laguerre differential equations are solved using the Laplace transform. The solution is found to be in exact agreement with that obtained using the power series method. In addition, some properties and some recursion relations of the Laguerre and associated Laguerre functions are discussed and proved. Then, the conformable Rodriguez’s formula and generating function are proposed.

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What this paper is about

In this paper, the conformable Laguerre and associated Laguerre differential equations are solved using the Laplace transform. The solution is found to be in exact agreement with that obtained using the power series method. In addition, some properties and some recursion relations of the Laguerre and associated Laguerre functions are discussed and proved. Then, the conformable Rodriguez’s formula and generating function are proposed.

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OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper, the conformable Laguerre and associated Laguerre differential equations are solved using the Laplace transform. The solution is found to be in exact agreement with that obtained using the power series method. In addition, some properties and some recursion relations of the Laguerre and associated Laguerre functions are discussed and proved. Then, the conformable Rodriguez’s formula and generating function are proposed.

Key concepts: Laguerre polynomials, Conformable matrix, Laguerre's method, Laplace transform, Mathematics, Mathematical analysis, Polynomial, Laplace transform applied to differential equations

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