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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/05.10.23.0010.01









  


  










Input Form





Sum[((n - m + p)!/Sqrt[(2 n + 1) (n + m)! (n - m)!]) SphericalHarmonicY[n, m, \[CurlyTheta], \[CurlyPhi]] w^(n - m), {n, m, Infinity}] == (p!/(2^(m + 1) Sqrt[Pi] m!)) (((-Sin[\[CurlyTheta]]) E^(I \[CurlyPhi]))^m/(1 - w Cos[\[CurlyTheta]])^ (p + 1)) Hypergeometric2F1[(p + 1)/2, p/2 + 1, m + 1, -((w Sin[\[CurlyTheta]])/(1 - w Cos[\[CurlyTheta]]))^2] /; m >= 0 && Element[p, Integers] && p >= 0 && Element[\[CurlyTheta], Reals] && Element[\[CurlyPhi], Reals] && Abs[w] < 1










Standard Form





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MathML Form







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</ci> </apply> <apply> <in /> <ci> &#977; </ci> <reals /> </apply> <apply> <in /> <ci> &#966; </ci> <reals /> </apply> <apply> <lt /> <apply> <abs /> <ci> w </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29