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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/07.37.06.0031.01









  


  










Input Form





SphericalHarmonicY[\[Lambda], \[Mu], \[CurlyTheta], \[CurlyPhi]] \[Proportional] E^(I \[CurlyPhi] \[Mu]) ((2^\[Lambda] Sqrt[2 \[Lambda] + 1] Sqrt[Gamma[\[Lambda] - \[Mu] + 1]] Sqrt[Gamma[\[Lambda] + \[Mu] + 1]] Sin[Pi (\[Mu] - \[Lambda])] Cos[\[CurlyTheta]]^(-\[Lambda] - 1))/ (Pi^(3/2) Gamma[-\[Lambda]] Gamma[2 + 2 \[Lambda]])) ((Cos[\[CurlyTheta]/2]^2)^(\[Mu]/2)/(Sin[\[CurlyTheta]/2]^2)^(\[Mu]/2)) (Log[Cos[\[CurlyTheta]]/2] - EulerGamma - PolyGamma[-\[Mu] - \[Lambda]] - PolyGamma[1 + \[Lambda]] + PolyGamma[2 + 2 \[Lambda]]) (1 + O[1/Cos[\[CurlyTheta]]]) + ((2^\[Lambda] Gamma[1/2 + \[Lambda]])/ (Sqrt[Pi] Gamma[1 - \[Mu] + \[Lambda]])) Cos[\[CurlyTheta]]^\[Lambda] ((Cos[\[CurlyTheta]/2]^2)^(\[Mu]/2)/(Sin[\[CurlyTheta]/2]^2)^(\[Mu]/2)) (1 + O[1/Cos[\[CurlyTheta]]]) /; Element[2 \[Lambda], Integers] && 2 \[Lambda] >= 0 && !Element[\[Lambda] - \[Mu], Integers]










Standard Form





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MathML Form







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</ci> </apply> </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





© 1998- Wolfram Research, Inc.