Linear Differential Equations and Orthogonal Polynomials: A Novel Approach

2002/03/11 by N. Gurappa, Prasanta K. Panigrahi, Gurappa, N. +3
Mathematics · Physics and Astronomy · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.math-ph/0203015

Typographical Error Corrected on Page1

arxiv created 2002/03/11 · arxiv updated 2009/11/30

Abstract

A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for the solutions of the known differential equations, the procedure enables one to derive various properties of the orthogonal polynomials and functions, in a unified manner. The method of generalization of the present approach to the multi-variate case is pointed out and also its connection with the well-known factorization technique. It is shown that, the generating functions and Rodriguez formulae emerge naturally in this method.

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