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variants of this functions
SphericalHarmonicY






Mathematica Notation

Traditional Notation









Hypergeometric Functions > SphericalHarmonicY[lambda,mu,theta,phi] > Series representations > Generalized power series > Expansions at cos(theta)==infinity





http://functions.wolfram.com/07.37.06.0026.02









  


  










Input Form





SphericalHarmonicY[\[Lambda], \[Mu], \[CurlyTheta], \[CurlyPhi]] \[Proportional] ((Sqrt[2 \[Lambda] + 1] Sqrt[Gamma[\[Lambda] - \[Mu] + 1]])/ (2 Pi Sqrt[Gamma[\[Lambda] + \[Mu] + 1]])) E^(I \[CurlyPhi] \[Mu]) ((Cos[\[CurlyTheta]/2]^2)^(\[Mu]/2)/(Sin[\[CurlyTheta]/2]^2)^(\[Mu]/2)) (((2^\[Lambda] (Cos[\[CurlyTheta]] - 1)^\[Lambda])/ Gamma[\[Lambda] - \[Mu] + 1]) Gamma[1/2 + \[Lambda]] (1 + (\[Mu] - \[Lambda])/(1 - Cos[\[CurlyTheta]]) + ((1 - \[Lambda]) (\[Mu] - \[Lambda]) (1 + \[Mu] - \[Lambda]))/ ((1 - 2 \[Lambda]) (1 - Cos[\[CurlyTheta]])^2) + \[Ellipsis]) + ((2^(-1 - \[Lambda]) (z - 1)^(-1 - \[Lambda]))/Gamma[-\[Mu] - \[Lambda]]) Gamma[-(1/2) - \[Lambda]] (1 + (1 + \[Mu] + \[Lambda])/ (1 - Cos[\[CurlyTheta]]) + ((2 + \[Lambda]) (1 + \[Mu] + \[Lambda]) (2 + \[Mu] + \[Lambda]))/((3 + 2 \[Lambda]) (Cos[\[CurlyTheta]] - 1)^ 2) + \[Ellipsis])) /; Abs[Sin[\[CurlyTheta]/2]] > 1 && !Element[2 \[Lambda], Integers]










Standard Form





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MathML Form







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</ci> <ci> &#955; </ci> </apply> <apply> <plus /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> <ci> &#955; </ci> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#955; </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> <and /> <apply> <gt /> <apply> <abs /> <apply> <sin /> <apply> <times /> <ci> &#977; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <notin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#955; </ci> </apply> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29