A generating function for the spherical harmonics in p dimensions
G.F. Torres del Castillo
Departamento de Física Matemática, Instituto de Ciencias, Universidad Autónoma de Puebla,72570 Puebla, Pue., México.
Received 13 November 2012; ]]> Accepted 25 January 2013
Abstract
A generating function for the spherical harmonics in three or more dimensions is given. This function allows us to find in a simple manner the explicit expressions for the spherical harmonics in three dimensions. The generating functions for the spherical harmonics given here are analogous to certain well-known generating functions for solutions of the wave equation.
Keywords: Spherical harmonics; generating functions; Laplace equation; wave equation.
Resumen
Se da una función generatriz para los armónicos esféricos en tres o más dimensiones. Esta función permite hallar en una forma simple las expresiones explícitas para los armónicos esféricos en tres dimensiones. Las funciones generatrices para los armónicos esféricos dadas aquí son análogas a ciertas funciones generatrices bien conocidas para soluciones de la ecuación de onda.
Descriptores: Armónicos esféricos; funciones generatrices; ecuación de Laplace; ecuación de onda.
]]> PACS: 02.30.Gp; 02.30.Jr; 02.30.Uu
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