On the Expansion of Harmonic Functions in Terms of Normal-Orthogonal Harmonic Polynomials

Autor:	Gaylord M. Merriman
Rok vydání:	1931
Předmět:	Classical orthogonal polynomials Pure mathematics Subharmonic function Gegenbauer polynomials Harmonic function Quantum harmonic oscillator General Mathematics Laguerre polynomials Biharmonic equation Harmonic measure Mathematics
Zdroj:	American Journal of Mathematics. 53:589
ISSN:	0002-9327
DOI:	10.2307/2371167
Popis:	Consiaer a closed, rectifiable Jordan curve, C, lying in the (x y)-plane, possessing continuous curvature, and of length u-. Let f(x,y) be a function which is harmonic inside C and continuous in the closed region 0 consisting of C and its interior. The present paper is concerned with the development of f(x,y) in terms of a set of harmonic polynomials Pm(x,y), which are linear combinations of the functions 1, x, y, x2 y2, Xyy . Let
Databáze:	OpenAIRE
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