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variants of this functions
JacobiP






Mathematica Notation

Traditional Notation









Polynomials > JacobiP[n,a,b,z] > Series representations > Generalized power series > Expansions at z==infinity > For the function itself > Expansions in 1/(1-z)





http://functions.wolfram.com/05.06.06.0015.01









  


  










Input Form





JacobiP[n, a, b, z] \[Proportional] (Pochhammer[1 + a + b + n, n]/(2^n n!)) (z - 1)^n (1 - (2 n (-a - n))/((-a - b - 2 n) (1 - z)) - (2 n (1 - n) (-a - n) (1 - a - n))/((-a - b - 2 n) (1 - a - b - 2 n) (1 - z)^2) - \[Ellipsis]) /; (Abs[z] -> Infinity) && !(Element[a + b + 2 n, Integers] && a + b + 2 n <= 0)










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["n_", ",", "a_", ",", "b_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["-", "n"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "+", "a", "+", "b", "+", "n"]], ",", "n"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "1"]], ")"]], "n"], " ", RowBox[List["(", RowBox[List["1", "-", FractionBox[RowBox[List["2", " ", "n", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "-", "n"]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", RowBox[List["2", " ", "n"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]]]]], "-", FractionBox[RowBox[List["2", " ", "n", " ", RowBox[List["(", RowBox[List["1", "-", "n"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "-", "n"]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", "a", "-", "n"]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", RowBox[List["2", " ", "n"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "-", "a", "-", "b", "-", RowBox[List["2", " ", "n"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]], "2"]]]], "-", "\[Ellipsis]"]], ")"]]]], RowBox[List["n", "!"]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "&&", RowBox[List["!", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", "n"]]]], "\[Element]", "Integers"]], "&&", RowBox[List[RowBox[List["a", "+", "b", "+", RowBox[List["2", " ", "n"]]]], "\[LessEqual]", "0"]]]], ")"]]]]]]]]]]]]










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





2001-10-29





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