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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==infinity





http://functions.wolfram.com/07.15.06.0026.01









  


  










Input Form





JacobiP[\[Nu], a, b, z] \[Proportional] (Pochhammer[1 + a + b + \[Nu], \[Nu]]/(2^\[Nu] Gamma[\[Nu] + 1])) (z - 1)^\[Nu] (1 + O[1/z]) - ((2^(a + b + \[Nu] + 1) Sin[\[Nu] Pi] Gamma[-a - b - 2 \[Nu] - 1] Gamma[a + \[Nu] + 1])/(Pi Gamma[-b - \[Nu]])) (z - 1)^(-a - b - \[Nu] - 1) (1 + O[1/z]) /; (Abs[z] -> Infinity) && !Element[a + b + 2 \[Nu], Integers]










Standard Form





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MathML Form







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</ci> </apply> </apply> <integers /> </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[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "+", "a", "+", "b", "+", "\[Nu]"]], ",", "\[Nu]"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], "\[Nu]"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", "z"], "]"]]]], ")"]]]], RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["a", "+", "b", "+", "\[Nu]", "+", "1"]]], " ", RowBox[List["Sin", "[", RowBox[List["\[Nu]", " ", "\[Pi]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", RowBox[List["2", " ", "\[Nu]"]], "-", "1"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["a", "+", "\[Nu]", "+", "1"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", "\[Nu]", "-", "1"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", "z"], "]"]]]], ")"]]]], RowBox[List["\[Pi]", " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "b"]], "-", "\[Nu]"]], "]"]]]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "&&", RowBox[List["!", RowBox[List[RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", "\[Nu]"]]]], "\[Element]", "Integers"]]]]]]]]]]]]










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





2001-10-29