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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 sin(theta/2)==0





http://functions.wolfram.com/05.10.06.0001.02









  


  










Input Form





SphericalHarmonicY[n, m, \[CurlyTheta], \[CurlyPhi]] \[Proportional] (Sqrt[(2 n + 1)/(4 Pi)] (Sqrt[Gamma[n - m + 1]]/Sqrt[Gamma[n + m + 1]]) E^(I \[CurlyPhi] m) (1/Gamma[1 - m] - ((m (1 - m) + 2 n (1 + n)) Sin[\[CurlyTheta]/2]^2)/(2 Gamma[2 - m]) + (1/(8 Gamma[3 - m])) (-5 m^3 + m^4 + 4 (-1 + n) n (1 + n) (2 + n) - 4 m^2 (-2 + n + n^2) + m (-4 + 8 n (1 + n))) Sin[\[CurlyTheta]/2]^4 - \[Ellipsis]))/(Sin[\[CurlyTheta]/2]^2)^(m/2) /; (Sin[\[CurlyTheta]/2] -> 0)










Standard Form





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MathML Form







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Rule Form





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2001-10-29





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