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variants of this functions
JacobiP




Mathematica Notation

Traditional Notation









Polynomials > JacobiP[n,a,b,z] > Representations through more general functions > Through Meijer G > Classical cases involving unit step theta





http://functions.wolfram.com/05.06.26.0015.01









  


  








Input Form





UnitStep[1 - Abs[z]] (1 - z)^(-n - a - b - 1) JacobiP[n, a, b, (1 + z)/(1 - z)] == (((-1)^n Gamma[-a - b - n])/n!) MeijerG[{{}, {-a - n, -a - b - n}}, {{0, -a}, {}}, z]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["UnitStep", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z_", "]"]]]], "]"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["1", "-", "z_"]], ")"]], RowBox[List[RowBox[List["-", "n_"]], "-", "a_", "-", "b_", "-", "1"]]], " ", RowBox[List["JacobiP", "[", RowBox[List["n_", ",", "a_", ",", "b_", ",", FractionBox[RowBox[List["1", "+", "z_"]], RowBox[List["1", "-", "z_"]]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "n"], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", "n"]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[RowBox[List["-", "a"]], "-", "n"]], ",", RowBox[List[RowBox[List["-", "a"]], "-", "b", "-", "n"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", RowBox[List["-", "a"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List["n", "!"]]]]]]]


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





2001-10-29