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variants of this functions
JacobiP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > JacobiP[nu,a,b,z] > Identities > Functional identities > Relations between contiguous functions > Recurrence relations





http://functions.wolfram.com/07.15.17.0024.01









  


  








Input Form





JacobiP[\[Nu], a, b, z] == ((z + 1)/2) JacobiP[\[Nu], a, b + 1, z] - ((z - 1)/2) JacobiP[\[Nu], a + 1, b, z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", "b", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[FractionBox[RowBox[List["z", "+", "1"]], "2"], " ", RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", RowBox[List["b", "+", "1"]], ",", "z"]], "]"]]]], "-", RowBox[List[FractionBox[RowBox[List["z", "-", "1"]], "2"], RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", RowBox[List["a", "+", "1"]], ",", "b", ",", "z"]], "]"]]]]]]]]]]








MathML Form







<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> &#957; </mi> <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> &#63449; </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msubsup> <mi> P </mi> <mi> &#957; </mi> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> , </mo> <mrow> <mi> b </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msubsup> <mi> P </mi> <mi> &#957; </mi> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> JacobiP </ci> <ci> &#957; </ci> <ci> a </ci> <ci> b </ci> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> JacobiP </ci> <ci> &#957; </ci> <ci> a </ci> <apply> <plus /> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <ci> JacobiP </ci> <ci> &#957; </ci> <apply> <plus /> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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


Date Added to functions.wolfram.com (modification date)





2007-05-02