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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 b==infinity





http://functions.wolfram.com/05.06.06.0020.01









  


  








Input Form





JacobiP[n, a, b, z] \[Proportional] (b^n/n!) ((z - 1)/2)^n (1 + (n (-1 + n + z + 3 n z + 2 a (1 + z)))/(2 b (-1 + z)) + (1/(24 b^2 (-1 + z)^2)) ((-1 + n) n (2 (-1 + z)^2 + 12 a^2 (1 + z)^2 + 3 (n + 3 n z)^2 + 12 a (1 + z) (-3 + n + z + 3 n z) + n (-31 + 17 (-2 + z) z))) + \[Ellipsis]) /; (Abs[b] -> Infinity)








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[SuperscriptBox["b", "n"], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["z", "-", "1"]], "2"], ")"]], "n"], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List["n", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "n", "+", "z", "+", RowBox[List["3", " ", "n", " ", "z"]], "+", RowBox[List["2", " ", "a", " ", RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]]]]]], ")"]]]], RowBox[List["2", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "n"]], ")"]], " ", "n", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"]]], "+", RowBox[List["12", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], "2"]]], "+", RowBox[List["3", " ", SuperscriptBox[RowBox[List["(", RowBox[List["n", "+", RowBox[List["3", " ", "n", " ", "z"]]]], ")"]], "2"]]], "+", RowBox[List["12", " ", "a", " ", RowBox[List["(", RowBox[List["1", "+", "z"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", "n", "+", "z", "+", RowBox[List["3", " ", "n", " ", "z"]]]], ")"]]]], "+", RowBox[List["n", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "31"]], "+", RowBox[List["17", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "z"]], ")"]], " ", "z"]]]], ")"]]]]]], ")"]]]], RowBox[List["24", " ", SuperscriptBox["b", "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], "2"]]]], "+", "\[Ellipsis]"]], ")"]]]], RowBox[List["n", "!"]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "b", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]


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





2002-03-07