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http://functions.wolfram.com/05.06.03.0007.01
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JacobiP[n, a, -a, z] == (Gamma[n + a + 1]/Gamma[n + 1])
((z + 1)^(a/2)/(z - 1)^(a/2)) LegendreP[n, -a, 3, z]
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Cell[BoxData[RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["n", ",", "a", ",", RowBox[List["-", "a"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["Gamma", "[", RowBox[List["n", "+", "a", "+", "1"]], "]"]], RowBox[List["Gamma", "[", RowBox[List["n", "+", "1"]], "]"]]], FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], RowBox[List["a", "/", "2"]]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List["a", "/", "2"]]]], RowBox[List["LegendreP", "[", RowBox[List["n", ",", RowBox[List["-", "a"]], ",", "3", ",", "z"]], "]"]]]]]]]]
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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> <msubsup> <mi> P </mi> <mi> n </mi> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mrow> <mo> - </mo> <mi> a </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> Γ </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mfrac> <mo> ⁢ </mo> <mfrac> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> a </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <msup> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> a </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <msubsup> <semantics> <mi> 𝔓 </mi> <annotation encoding='Mathematica'> TagBox["\[GothicCapitalP]", LegendreQ] </annotation> </semantics> <mi> n </mi> <mrow> <mo> - </mo> <mi> a </mi> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiP </ci> <ci> n </ci> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> a </ci> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <apply> <ci> LegendreQ </ci> <ci> 𝔓 </ci> </apply> <ci> n </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiP", "[", RowBox[List["n_", ",", "a_", ",", RowBox[List["-", "a_"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["n", "+", "a", "+", "1"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "+", "1"]], ")"]], RowBox[List["a", "/", "2"]]], " ", RowBox[List["LegendreP", "[", RowBox[List["n", ",", RowBox[List["-", "a"]], ",", "3", ",", "z"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["n", "+", "1"]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List["a", "/", "2"]]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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