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variants of this functions
LegendreQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,3,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/07.12.20.0012.02









  


  










Input Form





D[LegendreQ[\[Nu], \[Mu], 3, z], {z, n}] == (Pi/2) Csc[Pi \[Mu]] E^(Pi I \[Mu]) (((z + 1)^(\[Mu]/2)/(z - 1)^(\[Mu]/2 + n)) Gamma[1 + \[Mu]/2] Sum[Binomial[n, j] Hypergeometric2F1Regularized[-j, \[Mu]/2, 1 - j + \[Mu]/2, (z + 1)/(z - 1)] HypergeometricPFQRegularized[{1, -\[Nu], 1 + \[Nu]}, {1 - n + j, 1 - \[Mu]}, (1 - z)/2] ((z - 1)/(z + 1))^j, {j, 0, n}] - Pochhammer[1 + \[Nu] - \[Mu], 2 \[Mu]] ((z - 1)^(\[Mu]/2 - n)/ (z + 1)^(\[Mu]/2)) Gamma[1 - \[Mu]/2] Sum[Binomial[n, j] Hypergeometric2F1Regularized[-j, -(\[Mu]/2), 1 - j - \[Mu]/2, (z + 1)/(z - 1)] HypergeometricPFQRegularized[ {1, -\[Nu], 1 + \[Nu]}, {1 - n + j, 1 + \[Mu]}, (1 - z)/2] ((z - 1)/(z + 1))^j, {j, 0, n}]) /; Element[n, Integers] && n >= 0 && !Element[\[Mu], Integers]










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





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