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variants of this functions
SphericalHarmonicY






Mathematica Notation

Traditional Notation









Polynomials > SphericalHarmonicY[n,m,theta,phi] > Series representations > Generalized power series > Expansions at cos(theta)==infinity





http://functions.wolfram.com/05.10.06.0021.02









  


  










Input Form





SphericalHarmonicY[n, m, \[CurlyTheta], \[CurlyPhi]] \[Proportional] ((Sqrt[2 n + 1] Sqrt[Gamma[n - m + 1]])/(2 Pi Sqrt[Gamma[n + m + 1]])) E^(I \[CurlyPhi] m) ((Cos[\[CurlyTheta]/2]^2)^(m/2)/ (Sin[\[CurlyTheta]/2]^2)^(m/2)) (((2^n (Cos[\[CurlyTheta]] - 1)^n)/Gamma[n - m + 1]) Gamma[1/2 + n] (1 + (m - n)/(1 - Cos[\[CurlyTheta]]) + ((1 - n) (m - n) (1 + m - n))/ ((1 - 2 n) (1 - Cos[\[CurlyTheta]])^2) + \[Ellipsis]) + ((2^(-1 - n) (z - 1)^(-1 - n))/Gamma[-m - n]) Gamma[-(1/2) - n] (1 + (1 + m + n)/(1 - Cos[\[CurlyTheta]]) + ((2 + n) (1 + m + n) (2 + m + n))/((3 + 2 n) (Cos[\[CurlyTheta]] - 1)^ 2) + \[Ellipsis])) /; (Abs[Cos[\[CurlyTheta]]] -> Infinity)










Standard Form





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MathML Form







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</ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <ci> m </ci> <ci> n </ci> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> m </ci> <ci> n </ci> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> n </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <cos /> <ci> &#977; </ci> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </apply> </apply> <apply> <abs /> <apply> <cos /> <ci> &#977; </ci> </apply> </apply> </apply> <infinity /> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998-2014 Wolfram Research, Inc.