JacobiP[2, a, b, z] == (1/8) ((3 + a + b) (4 + a + b) z^2 + 2 (3 a + a^2 - b (3 + b)) z - 4 + a^2 - b + b^2 - a (1 + 2 b))

Cell[BoxData[RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["2", ",", "a", ",", "b", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["3", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "a", "+", "b"]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "a"]], "+", SuperscriptBox["a", "2"], "-", RowBox[List["b", " ", RowBox[List["(", RowBox[List["3", "+", "b"]], ")"]]]]]], ")"]], " ", "z"]], "-", "4", "+", SuperscriptBox["a", "2"], "-", "b", "+", SuperscriptBox["b", "2"], "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "b"]]]], ")"]]]]]], ")"]]]]]]]]

<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> <mn> 2 </mn> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 8 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> + </mo> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> + </mo> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 4 </mn> <mo> + </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mi> b </mi> <mo> + </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiP </ci> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> b </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 8 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> 3 </cn> <ci> a </ci> <ci> b </ci> </apply> <apply> <plus /> <cn type='integer'> 4 </cn> <ci> a </ci> <ci> b </ci> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> a </ci> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <plus /> <cn type='integer'> 3 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> <ci> z </ci> </apply> <cn type='integer'> -4 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiP", "[", RowBox[List["2", ",", "a_", ",", "b_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["3", "+", "a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List["4", "+", "a", "+", "b"]], ")"]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", "a"]], "+", SuperscriptBox["a", "2"], "-", RowBox[List["b", " ", RowBox[List["(", RowBox[List["3", "+", "b"]], ")"]]]]]], ")"]], " ", "z"]], "-", "4", "+", SuperscriptBox["a", "2"], "-", "b", "+", SuperscriptBox["b", "2"], "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "b"]]]], ")"]]]]]], ")"]]]]]]]]

2001-10-29