|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
http://functions.wolfram.com/07.15.03.0005.01
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
JacobiP[\[Nu], a, a, z] == (Pochhammer[a + 1, \[Nu]]
GegenbauerC[\[Nu], a + 1/2, z])/Pochhammer[2 a + 1, \[Nu]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Cell[BoxData[RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", "a", ",", "z"]], "]"]], "\[Equal]", FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["a", "+", "1"]], ",", "\[Nu]"]], "]"]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", "+", FractionBox["1", "2"]]], ",", "z"]], "]"]]]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["2", " ", "a"]], "+", "1"]], ",", "\[Nu]"]], "]"]]]]]]]
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
<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> ν </mi> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> ν </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List["a", "+", "1"]], ")"]], "\[Nu]"], Pochhammer] </annotation> </semantics> <mtext> </mtext> </mrow> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> ν </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "+", "1"]], ")"]], "\[Nu]"], Pochhammer] </annotation> </semantics> </mfrac> <mo> ⁢ </mo> <mrow> <msubsup> <mi> C </mi> <mi> ν </mi> <mrow> <mi> a </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiP </ci> <ci> ν </ci> <ci> a </ci> <ci> a </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Pochhammer </ci> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <ci> ν </ci> </apply> <apply> <power /> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <cn type='integer'> 1 </cn> </apply> <ci> ν </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> C </ci> <ci> ν </ci> </apply> <apply> <plus /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
|
|
|
|
|
|
|
|
|
|
| |
|
|
|
|
| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiP", "[", RowBox[List["\[Nu]_", ",", "a_", ",", "a_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["a", "+", "1"]], ",", "\[Nu]"]], "]"]], " ", RowBox[List["GegenbauerC", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", "+", FractionBox["1", "2"]]], ",", "z"]], "]"]]]], RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List[RowBox[List["2", " ", "a"]], "+", "1"]], ",", "\[Nu]"]], "]"]]]]]]] |
|
|
|
|
|
|
|
|
|
|
|
Date Added to functions.wolfram.com (modification date)
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
){kind=small}
