Generating Functions for Lacunary Legendre and Legendre-like Polynomials

2020/02/13 by Silvia Licciardi, Licciardi, S., G. Dattoli +3
Computer Science · Mathematics · Physics and Astronomy · #05A40 #33B10 #33B15 #33C45 #33C52 #33C65 #33C99 #42C05 #44A99 #47A62 #47B99 #Advanced Mathematical Theories and Applications #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2002.05722

openalex publication_date 2020/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The use of operational methods of different nature is shown to be a fairly powerful tool to study different problems regarding the theory of Legendre and Legendre-like polynomials. We show how the use of the well known integral representations linking Hermite and Legendre like polynomials and of operational technique allow the derivation of new properties regarding the generating functions, repeated derivatives of irrational functions and so on. We finally extend the method of the integral transform to functions with more than one variable and derive new expansion criteria of a given function in terms of Legendre polynomials.

Citations

• The scaling properties and the multiple derivative of Legendre\n polynomials

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