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Chapter 2: Expansions with orthogonal polynomials
https://doi.org/10.1142/9789814635974_0002Cited by:0 (Source: Crossref)
Abstract:
In this chapter, we present methods of expansions of functions by projections in bases of squared integrable functions with respect to real measures. We define Laguerre, Hermite and Legendre orthonormal polynomials and recursive methods for their calculus, with their graphs. The conditions for the convergence of the expansions of functions in polynomial series depend on the properties of the measures defining their orthogonality. Several generalizations to the real line and the plane and their differential equations are presented.
