Linear Differential Equations and Orthogonal Polynomials: A Novel Approach

Details Linear Differential Equations and Orthogonal Polynomials: A Novel Approach Linear Differential Equations and Orthogonal Polynomials: A Novel Approach

2002-03-11

arxiv.org/abs/math-ph/0203015v1

Physics

Mathematical Physics

Typographical Error Corrected on Page1

Scientific paper

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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