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variants of this functions
JacobiP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > JacobiP[nu,a,b,z] > Representations through more general functions > Through hypergeometric functions > Involving 2F1





http://functions.wolfram.com/07.15.26.0003.01









  


  










Input Form





JacobiP[\[Nu], a, b, z] == (Gamma[-b]/(Gamma[\[Nu] + 1] Gamma[-b - \[Nu]])) HypergeometricPFQ[{-\[Nu], a + b + \[Nu] + 1}, {b + 1}, (z + 1)/2] - (((Sin[\[Nu] Pi] Gamma[b] Gamma[a + \[Nu] + 1])/ (Pi Gamma[a + b + \[Nu] + 1])) HypergeometricPFQ[ {a + \[Nu] + 1, -b - \[Nu]}, {1 - b}, (z + 1)/2])/((z + 1)/2)^b /; !Element[b, Integers]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["JacobiP", "[", RowBox[List["\[Nu]_", ",", "a_", ",", "b_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["-", "b"]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List["a", "+", "b", "+", "\[Nu]", "+", "1"]]]], "}"]], ",", RowBox[List["{", RowBox[List["b", "+", "1"]], "}"]], ",", FractionBox[RowBox[List["z", "+", "1"]], "2"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "b"]], "-", "\[Nu]"]], "]"]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Sin", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]], " ", RowBox[List["Gamma", "[", "b", "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["a", "+", "\[Nu]", "+", "1"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["z", "+", "1"]], "2"], ")"]], RowBox[List["-", "b"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["a", "+", "\[Nu]", "+", "1"]], ",", RowBox[List[RowBox[List["-", "b"]], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", "b"]], "}"]], ",", FractionBox[RowBox[List["z", "+", "1"]], "2"]]], "]"]]]], RowBox[List["\[Pi]", " ", RowBox[List["Gamma", "[", RowBox[List["a", "+", "b", "+", "\[Nu]", "+", "1"]], "]"]]]]]]], "/;", RowBox[List["!", RowBox[List["b", "\[Element]", "Integers"]]]]]]]]]]










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





2001-10-29