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http://functions.wolfram.com/07.11.20.0003.01
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D[LegendreQ[\[Nu], \[Mu], 2, z], \[Nu]] ==
(Pi/2) Csc[\[Mu] Pi] Pochhammer[1 - \[Mu] + \[Nu], 2 \[Mu]]
(PolyGamma[1 - \[Mu] + \[Nu]] - PolyGamma[1 + \[Mu] + \[Nu]])
LegendreP[\[Nu], -\[Mu], 2, z] +
((1 + 2 \[Nu])/(4 Gamma[1 - \[Mu] + \[Nu]])) ((1 - z)^(\[Mu]/2 + 1)/
(1 + z)^(\[Mu]/2)) (((1 + z)^\[Mu]/(1 - z)^\[Mu]) Cos[\[Mu] Pi]
Gamma[\[Mu] - 1] Gamma[1 - \[Mu] + \[Nu]] HypergeometricPFQ[
{{1 - \[Nu], 2 + \[Nu]}, {1}, {1, -\[Nu], 1 + \[Nu]}},
{{2, 2 - \[Mu]}, {}, {2 + \[Nu], 1 - \[Nu]}}, (1 - z)/2, (1 - z)/2] +
Gamma[-1 - \[Mu]] Gamma[1 + \[Mu] + \[Nu]] HypergeometricPFQ[
{{1 - \[Nu], 2 + \[Nu]}, {1}, {1, -\[Nu], 1 + \[Nu]}},
{{2, 2 + \[Mu]}, {}, {2 + \[Nu], 1 - \[Nu]}}, (1 - z)/2,
(1 - z)/2]) /; !Element[\[Mu], Integers]
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Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", "\[Nu]"], RowBox[List["LegendreQ", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", "2", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], RowBox[List["Csc", "[", RowBox[List["\[Mu]", " ", "\[Pi]"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "\[Mu]", "+", "\[Nu]"]], ",", RowBox[List["2", "\[Mu]"]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["PolyGamma", "[", RowBox[List["1", "-", "\[Mu]", "+", "\[Nu]"]], "]"]], "-", RowBox[List["PolyGamma", "[", RowBox[List["1", "+", "\[Mu]", "+", "\[Nu]"]], "]"]]]], ")"]], " ", RowBox[List["LegendreP", "[", RowBox[List["\[Nu]", ",", RowBox[List["-", "\[Mu]"]], ",", "2", ",", "z"]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List["1", "+", RowBox[List["2", " ", "\[Nu]"]]]], RowBox[List["4", " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Mu]", "+", "\[Nu]"]], "]"]]]]], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], RowBox[List[RowBox[List["\[Mu]", "/", "2"]], "+", "1"]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], RowBox[List["\[Mu]", "/", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "\[Mu]"], SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], "\[Mu]"]], " ", RowBox[List["Cos", "[", RowBox[List["\[Mu]", " ", "\[Pi]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["\[Mu]", "-", "1"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Mu]", "+", "\[Nu]"]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", RowBox[List["2", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["-", "\[Nu]"]], ",", RowBox[List["1", "+", "\[Nu]"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["2", "-", "\[Mu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", RowBox[List["1", "-", "\[Nu]"]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]]]], "+", RowBox[List[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "1"]], "-", "\[Mu]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Mu]", "+", "\[Nu]"]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", RowBox[List["2", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", "1", "}"]], ",", RowBox[List["{", RowBox[List["1", ",", RowBox[List["-", "\[Nu]"]], ",", RowBox[List["1", "+", "\[Nu]"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", ",", RowBox[List["2", "+", "\[Mu]"]]]], "}"]], ",", RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "+", "\[Nu]"]], ",", RowBox[List["1", "-", "\[Nu]"]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"], ",", FractionBox[RowBox[List["1", "-", "z"]], "2"]]], "]"]]]]]], ")"]]]]]]]], "/;", " ", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["\[Mu]", ",", "Integers"]], "]"]], "]"]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mfrac> <mrow> <mo> ∂ </mo> <mrow> <msubsup> <semantics> <mi> Q </mi> <annotation encoding='Mathematica'> TagBox["Q", LegendreQ] </annotation> </semantics> <mi> ν </mi> <mi> μ </mi> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox["z", HoldComplete[LegendreQ, 2]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> <mrow> <mo> ∂ </mo> <mi> ν </mi> </mrow> </mfrac> <mo> ⩵ </mo> <mrow> <mrow> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> ν </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mi> μ </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> ⁢ </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mi> μ </mi> <mo> / </mo> <mn> 2 </mn> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> </msup> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> μ </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mi> cos </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> μ </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> μ </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mi> μ </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mi> μ </mi> </msup> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mi> μ </mi> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <msubsup> <mi> F </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mn> 0 </mn> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mn> 1 </mn> <mo> ⁢ </mo> <mn> 3 </mn> </mrow> </msubsup> <mo> ( </mo> <mrow> <mrow> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ν </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mn> 1 </mn> <mo> ; </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 2 </mn> <mo> , </mo> <mrow> <mrow> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> μ </mi> </mrow> <mo> ; </mo> </mrow> <mo> ; </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mrow> <mo> , </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ν </mi> </mrow> <mo> ; </mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo> ⁢ </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> μ </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> μ </mi> <mo> + </mo> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <mi> F </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mn> 0 </mn> <mo> ⁢ </mo> <mn> 2 </mn> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mn> 1 </mn> <mo> ⁢ </mo> <mn> 3 </mn> </mrow> </msubsup> <mo> ( </mo> <mrow> <mrow> <mtable> <mtr> <mtd> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ν </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mo> ; </mo> <mn> 1 </mn> <mo> ; </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mi> ν </mi> </mrow> <mo> , </mo> <mrow> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ; </mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn> 2 </mn> <mo> , </mo> <mrow> <mrow> <mrow> <mn> 2 </mn> <mo> + </mo> <mi> μ </mi> </mrow> <mo> ; </mo> </mrow> <mo> ; </mo> <mrow> <mi> ν </mi> <mo> + </mo> <mn> 2 </mn> </mrow> </mrow> <mo> , </mo> <mrow> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ν </mi> </mrow> <mo> ; </mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo> ⁢ </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mtext> </mtext> <mo> + </mo> <mrow> <mfrac> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <mi> csc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> μ </mi> <mo> ⁢ </mo> <mi> π </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mi> μ </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> μ </mi> </mrow> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "-", "\[Mu]", "+", "1"]], ")"]], RowBox[List["2", " ", "\[Mu]"]]], Pochhammer] </annotation> </semantics> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mi> ν </mi> <mo> - </mo> <mi> μ </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <semantics> <mi> ψ </mi> <annotation encoding='Mathematica'> TagBox["\[Psi]", PolyGamma] </annotation> </semantics> <mo> ( </mo> <mrow> <mi> μ </mi> <mo> + </mo> <mi> ν </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msubsup> <semantics> <mi> P </mi> <annotation encoding='Mathematica'> TagBox["P", LegendreP] </annotation> </semantics> <mi> ν </mi> <mrow> <mo> - </mo> <mi> μ </mi> </mrow> </msubsup> <mo> ( </mo> <semantics> <mi> z </mi> <annotation encoding='Mathematica'> TagBox["z", HoldComplete[LegendreP, 2]] </annotation> </semantics> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> μ </mi> <mo> ∉ </mo> <mi> ℤ </mi> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> FormBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ∂ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <apply> <ci> TagBox </ci> <ms> Q </ms> <ci> LegendreQ </ci> </apply> <ms> ν </ms> <ms> μ </ms> </apply> <ms> ( </ms> <apply> <ci> TagBox </ci> <ms> z </ms> <apply> <ci> HoldComplete </ci> <ci> LegendreQ </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> ∂ </ms> <ms> ν </ms> </list> </apply> </apply> <ms> ⩵ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> ν </ms> </list> </apply> <ms> + </ms> <ms> 1 </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> 4 </ms> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> ν </ms> <ms> - </ms> <ms> μ </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </apply> <apply> <ci> FractionBox </ci> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> z </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> μ </ms> <ms> / </ms> <ms> 2 </ms> </list> </apply> <ms> + </ms> <ms> 1 </ms> </list> </apply> </apply> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> + </ms> <ms> z </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> μ </ms> <ms> / </ms> <ms> 2 </ms> </list> </apply> </apply> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> cos </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> μ </ms> <ms> π </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> μ </ms> <ms> - </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> ν </ms> <ms> - </ms> <ms> μ </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> FractionBox </ci> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> + </ms> <ms> z </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> μ </ms> </apply> <apply> <ci> SuperscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> z </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> μ </ms> </apply> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <ms> F </ms> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> 0 </ms> <ms> 2 </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> 1 </ms> <ms> 3 </ms> </list> </apply> </apply> <ms> [ </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> GridBox </ci> <list> <list> <apply> <ci> ErrorBox </ci> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> ν </ms> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ν </ms> <ms> + </ms> <ms> 2 </ms> </list> </apply> <ms> ; </ms> <ms> 1 </ms> <ms> ; </ms> <ms> 1 </ms> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> ν </ms> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ν </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> ; </ms> </list> </apply> </list> </apply> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> - </ms> <ms> μ </ms> </list> </apply> <ms> ; </ms> </list> </apply> <ms> ; </ms> <apply> <ci> RowBox </ci> <list> <ms> ν </ms> <ms> + </ms> <ms> 2 </ms> </list> </apply> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> ν </ms> </list> </apply> <ms> ; </ms> </list> </apply> </list> </apply> </list> </list> </apply> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> z </ms> </list> </apply> <ms> 2 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> z </ms> </list> </apply> <ms> 2 </ms> </apply> <ms> ] </ms> </list> </apply> </list> </apply> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> μ </ms> </list> </apply> <ms> - </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> Γ </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> μ </ms> <ms> + </ms> <ms> ν </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <ms> F </ms> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> 0 </ms> <ms> 2 </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> 1 </ms> <ms> 3 </ms> </list> </apply> </apply> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> GridBox </ci> <list> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> ν </ms> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ν </ms> <ms> + </ms> <ms> 2 </ms> </list> </apply> <ms> ; </ms> <ms> 1 </ms> <ms> ; </ms> <ms> 1 </ms> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> ν </ms> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> ν </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> ; </ms> </list> </apply> </list> </apply> </list> <list> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> + </ms> <ms> μ </ms> </list> </apply> <ms> ; </ms> </list> </apply> <ms> ; </ms> <apply> <ci> RowBox </ci> <list> <ms> ν </ms> <ms> + </ms> <ms> 2 </ms> </list> </apply> </list> </apply> <ms> , </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> ν </ms> </list> </apply> <ms> ; </ms> </list> </apply> </list> </apply> </list> </list> </apply> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> z </ms> </list> </apply> <ms> 2 </ms> </apply> </list> </apply> <ms> , </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> 1 </ms> <ms> - </ms> <ms> z </ms> </list> </apply> <ms> 2 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> + </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> π </ms> <apply> <ci> RowBox </ci> <list> <ms> csc </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> μ </ms> <ms> π </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> 2 </ms> </apply> <apply> <ci> TagBox </ci> <apply> <ci> SubscriptBox </ci> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> ν </ms> <ms> - </ms> <ms> μ </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> </ms> <ms> μ </ms> </list> </apply> </apply> <ci> Pochhammer </ci> </apply> <apply> <ci> RowBox </ci> <list> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <apply> <ci> TagBox </ci> <ms> ψ </ms> <ci> PolyGamma </ci> </apply> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> ν </ms> <ms> - </ms> <ms> μ </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> <ms> - </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> TagBox </ci> <ms> ψ </ms> <ci> PolyGamma </ci> </apply> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> μ </ms> <ms> + </ms> <ms> ν </ms> <ms> + </ms> <ms> 1 </ms> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> SubsuperscriptBox </ci> <apply> <ci> TagBox </ci> <ms> P </ms> <ci> LegendreP </ci> </apply> <ms> ν </ms> <apply> <ci> RowBox </ci> <list> <ms> - </ms> <ms> μ </ms> </list> </apply> </apply> <ms> ( </ms> <apply> <ci> TagBox </ci> <ms> z </ms> <apply> <ci> HoldComplete </ci> <ci> LegendreP </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ms> ) </ms> </list> </apply> </list> </apply> </list> </apply> </list> </apply> <ms> /; </ms> <apply> <ci> RowBox </ci> <list> <ms> μ </ms> <ms> ∉ </ms> <ms> ℤ </ms> </list> </apply> </list> </apply> <ci> TraditionalForm </ci> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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