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variants of this functions
JacobiP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > JacobiP[nu,a,b,z] > General characteristics > Symmetries and periodicities > Mirror symmetry





http://functions.wolfram.com/07.15.04.0004.02









  


  








Input Form





JacobiP[Conjugate[\[Nu]], Conjugate[a], Conjugate[b], Conjugate[z]] == Conjugate[JacobiP[\[Nu], a, b, z]] /; !IntervalMemberQ[Interval[{-Infinity, -1}], z]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["JacobiP", "[", RowBox[List[RowBox[List["Conjugate", "[", "\[Nu]", "]"]], ",", RowBox[List["Conjugate", "[", "a", "]"]], ",", RowBox[List["Conjugate", "[", "b", "]"]], ",", RowBox[List["Conjugate", "[", "z", "]"]]]], "]"]], "\[Equal]", RowBox[List["Conjugate", "[", RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", "b", ",", "z"]], "]"]], "]"]]]], "/;", RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "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> <mrow> <msubsup> <mi> P </mi> <mover> <mi> &#957; </mi> <mo> _ </mo> </mover> <mrow> <mo> ( </mo> <mrow> <mover> <mi> a </mi> <mo> _ </mo> </mover> <mo> , </mo> <mover> <mi> b </mi> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mover> <mi> z </mi> <mo> _ </mo> </mover> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <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> </mover> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mrow> <msubsup> <mi> P </mi> <mover> <mi> &#957; </mi> <mo> _ </mo> </mover> <mrow> <mo> ( </mo> <mrow> <mover> <mi> a </mi> <mo> _ </mo> </mover> <mo> , </mo> <mover> <mi> b </mi> <mo> _ </mo> </mover> </mrow> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mover> <mi> z </mi> <mo> _ </mo> </mover> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mover> <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> </mover> </mrow> <mo> /; </mo> <mrow> <mi> z </mi> <mo> &#8713; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> &#8734; </mi> </mrow> <mo> , </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiP", "[", RowBox[List[RowBox[List["Conjugate", "[", "\[Nu]_", "]"]], ",", RowBox[List["Conjugate", "[", "a_", "]"]], ",", RowBox[List["Conjugate", "[", "b_", "]"]], ",", RowBox[List["Conjugate", "[", "z_", "]"]]]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Conjugate", "[", RowBox[List["JacobiP", "[", RowBox[List["\[Nu]", ",", "a", ",", "b", ",", "z"]], "]"]], "]"]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", RowBox[List["-", "1"]]]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29