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variants of this functions
JacobiP




Mathematica Notation

Traditional Notation









Hypergeometric Functions > JacobiP[nu,a,b,z] > Series representations > Generalized power series > Expansions at z==0





http://functions.wolfram.com/07.15.06.0001.01









  


  








Input Form





JacobiP[\[Nu], a, b, z] == (HypergeometricPFQ[{-\[Nu], -b - \[Nu]}, {1 + a}, -1] + ((\[Nu] (1 + a + b + \[Nu]))/(1 + a)) HypergeometricPFQ[ {1 - \[Nu], -b - \[Nu]}, {2 + a}, -1] z + (((\[Nu] - 1) \[Nu] (1 + a + b + \[Nu]) (2 + a + b + \[Nu]))/ (2 (1 + a) (2 + a))) HypergeometricPFQ[{2 - \[Nu], -b - \[Nu]}, {3 + a}, -1] z^2 + \[Ellipsis])/2^\[Nu] /; Abs[z] < 1








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[SuperscriptBox["2", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List[RowBox[List["-", "b"]], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", "a"]], "}"]], ",", RowBox[List["-", "1"]]]], "]"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", " ", RowBox[List["(", RowBox[List["1", "+", "a", "+", "b", "+", "\[Nu]"]], ")"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", RowBox[List[RowBox[List["-", "b"]], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", RowBox[List["2", "+", "a"]], "}"]], ",", RowBox[List["-", "1"]]]], "]"]], " ", "z"]], RowBox[List["1", "+", "a"]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["\[Nu]", "-", "1"]], ")"]], " ", "\[Nu]", " ", RowBox[List["(", RowBox[List["1", "+", "a", "+", "b", "+", "\[Nu]"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "a", "+", "b", "+", "\[Nu]"]], ")"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["2", "-", "\[Nu]"]], ",", RowBox[List[RowBox[List["-", "b"]], "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["{", RowBox[List["3", "+", "a"]], "}"]], ",", RowBox[List["-", "1"]]]], "]"]], " ", SuperscriptBox["z", "2"]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["1", "+", "a"]], ")"]], " ", RowBox[List["(", RowBox[List["2", "+", "a"]], ")"]]]]], "+", "\[Ellipsis]"]], ")"]]]], "/;", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "<", "1"]]]]]]]]


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





2001-10-29