Fourier Series and Orthogonal Polynomials

Thistextforundergraduateandgraduatestudentsillustratesthefundamentalsimplicityofthepropertiesoforthogonalfunctionsandtheirdevelopmentsinrelatedseries.StartingwithadefinitionandexplanationoftheelementsofFourierseries,thetextfollowswithexaminationsofLegendrepolynomialsandBesselfunctions.BoundaryvalueproblemsconsiderFourierseriesinconjunctionwithLaplace'sequationinaninfinitestripandinarectangle,withavibratingstring,inthreedimensions,inasphere,andinothercircumstances.AnoverviewofPearsonfrequencyfunctionsisfollowedbychaptersonorthogonal,Jacobi,Hermite,andLaguerrepolynomials,andthetextconcludeswithachapteronconvergence.1941edition.,