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variants of this functions
JacobiP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > JacobiP[nu,a,b,z] > General characteristics > Branch points > With respect to z





http://functions.wolfram.com/07.15.04.0012.01









  


  








Input Form





BranchPoints[JacobiP[\[Nu], a, b, z], z] == {-1, ComplexInfinity} /; NonTerminatingHypergeometricSeriesQ[{-\[Nu], a + b + \[Nu] + 1}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", "b", ",", "z"]], "]"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "ComplexInfinity"]], "}"]]]], "/;", RowBox[List["NonTerminatingHypergeometricSeriesQ", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List["a", "+", "b", "+", "\[Nu]", "+", "1"]]]], "}"]], "]"]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msub> <mi> &#8492;&#119979; </mi> <mi> z </mi> </msub> <mo> ( </mo> <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> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mover> <mi> &#8734; </mi> <mo> ~ </mo> </mover> </mrow> <mo> } </mo> </mrow> </mrow> <mo> /; </mo> <mrow> <mi> &#119977;&#119983; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mo> { </mo> <mrow> <mrow> <mo> - </mo> <mi> &#957; </mi> </mrow> <mo> , </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mi> &#957; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> </mrow> <mo> } </mo> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <apply> <ci> Subscript </ci> <ci> &#8492;&#119979; </ci> <ci> z </ci> </apply> <apply> <ci> JacobiP </ci> <ci> &#957; </ci> <ci> a </ci> <ci> b </ci> <ci> z </ci> </apply> </apply> <list> <cn type='integer'> -1 </cn> <apply> <ci> OverTilde </ci> <infinity /> </apply> </list> </apply> <apply> <ci> &#119977;&#119983; </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <apply> <plus /> <ci> a </ci> <ci> b </ci> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> </list> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BranchPoints", "[", RowBox[List[RowBox[List["JacobiP", "[", RowBox[List["\[Nu]_", ",", "a_", ",", "b_", ",", "z_"]], "]"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "ComplexInfinity"]], "}"]], "/;", RowBox[List["NonTerminatingHypergeometricSeriesQ", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List["a", "+", "b", "+", "\[Nu]", "+", "1"]]]], "}"]], "]"]]]]]]]]


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





2001-10-29