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variants of this functions
SphericalHarmonicY






Mathematica Notation

Traditional Notation









Polynomials > SphericalHarmonicY[n,m,theta,phi] > Summation > Infinite summation





http://functions.wolfram.com/05.10.23.0012.01









  


  










Input Form





Sum[Sqrt[(n - m)!/((2 n + 1) (n + m)!)] LaguerreL[n - m, 2 m, z] SphericalHarmonicY[n, m, \[CurlyTheta], \[CurlyPhi]] w^(n - m), {n, m, Infinity}] == (1/(2^(m + 1) Sqrt[Pi] m!)) (((-Sin[\[CurlyTheta]]) E^(I \[CurlyPhi]))^m/ (1 - 2 w Cos[\[CurlyTheta]] + w^2)^(m + 1/2)) Exp[-((z w (Cos[\[CurlyTheta]] - w))/(1 - 2 w Cos[\[CurlyTheta]] + w^2))] Hypergeometric0F1[m + 1, -((z^2 w^2 Sin[\[CurlyTheta]]^2)/ (4 (1 - 2 w Cos[\[CurlyTheta]] + w^2)^2))] /; m >= 0 && Element[\[CurlyTheta], Reals] && Element[\[CurlyPhi], Reals] && Abs[w] < 1










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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