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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==-1





http://functions.wolfram.com/07.15.06.0018.01









  


  








Input Form





JacobiP[\[Nu], a, b, z] \[Proportional] ((-(((b - 1)! Sin[Pi \[Nu]] Gamma[a + \[Nu] + 1])/ (Pi Gamma[a + b + \[Nu] + 1]))) (1 + O[z + 1]))/((z + 1)/2)^b + ((-1)^(b - 1)/(b! Gamma[\[Nu] + 1] Gamma[-b - \[Nu]])) (Log[(z + 1)/2] + EulerGamma - PolyGamma[1 + b] + PolyGamma[-\[Nu]] + PolyGamma[1 + a + b + \[Nu]]) (1 + O[z + 1]) /; (z -> -1) && Element[b, Integers] && b > 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["\[Nu]_", ",", "a_", ",", "b_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "-", "1"]], ")"]], "!"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["a", "+", "\[Nu]", "+", "1"]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["z", "+", "1"]], "2"], ")"]], RowBox[List["-", "b"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "+", "1"]], "]"]]]], ")"]]]], RowBox[List["\[Pi]", " ", RowBox[List["Gamma", "[", RowBox[List["a", "+", "b", "+", "\[Nu]", "+", "1"]], "]"]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["b", "-", "1"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["Log", "[", FractionBox[RowBox[List["z", "+", "1"]], "2"], "]"]], "+", "EulerGamma", "-", RowBox[List["PolyGamma", "[", RowBox[List["1", "+", "b"]], "]"]], "+", RowBox[List["PolyGamma", "[", RowBox[List["-", "\[Nu]"]], "]"]], "+", RowBox[List["PolyGamma", "[", RowBox[List["1", "+", "a", "+", "b", "+", "\[Nu]"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", RowBox[List["z", "+", "1"]], "]"]]]], ")"]]]], RowBox[List[RowBox[List["b", "!"]], " ", RowBox[List["Gamma", "[", RowBox[List["\[Nu]", "+", "1"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "b"]], "-", "\[Nu]"]], "]"]]]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List["z", "\[Rule]", RowBox[List["-", "1"]]]], ")"]], "&&", RowBox[List["b", "\[Element]", "Integers"]], "&&", RowBox[List["b", ">", "0"]]]]]]]]]]


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





2001-10-29