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variants of this functions
SphericalHarmonicY




Mathematica Notation

Traditional Notation









Hypergeometric Functions > SphericalHarmonicY[lambda,mu,theta,phi] > Integral representations > Integral representations of negative integer order





http://functions.wolfram.com/07.37.07.0009.01









  


  








Input Form





SphericalHarmonicY[n, m, \[CurlyTheta], \[CurlyPhi]] == ((-1)^(m + n)/(n - m)!) r^(n + 1) Sqrt[((2 n + 1) (n - m)!)/(4 Pi (n + m)!)] Nest[Function[f, D[f, x] + I D[f, y]], D[1/r, {z, n - m}], m] /; r == Sqrt[x^2 + y^2 + z^2] && x == r Cos[\[CurlyPhi]] Sin[\[CurlyTheta]] && y == r Sin[\[CurlyPhi]] Sin[\[CurlyTheta]] && z == r Cos[\[CurlyTheta]] && Element[n, Integers] && n >= 0 && Element[m, Integers] && m >= 0 && m <= n








Standard Form





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MathML Form







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Rule Form





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





2001-10-29