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variants of this functions
Hypergeometric2F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric2F1[a,b,c,z] > Representations through more general functions > Through Meijer G > Classical cases involving algebraic functions with cubics in arguments





http://functions.wolfram.com/07.23.26.0052.01









  


  








Input Form





((8 + 9 z) Hypergeometric2F1[a, 1/3 + a, 3/2, (8 + 9 z)^2/(4 + 3 z)^3])/ (4 + 3 z)^(3 a) == ((3^(2 - 3 a) Sqrt[Pi])/(2 Gamma[4/3 - a] Gamma[-1 + 3 a])) MeijerG[{{2 - 3 a}, {5/2 - 3 a}}, {{7/3 - 4 a, 0}, {}}, z] /; Abs[z] > 1 || Re[z] >= 0








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["4", "+", RowBox[List["3", " ", "z_"]]]], ")"]], RowBox[List[RowBox[List["-", "3"]], " ", "a_"]]], " ", RowBox[List["(", RowBox[List["8", "+", RowBox[List["9", " ", "z_"]]]], ")"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List["a_", ",", RowBox[List[FractionBox["1", "3"], "+", "a_"]], ",", FractionBox["3", "2"], ",", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["8", "+", RowBox[List["9", " ", "z_"]]]], ")"]], "2"], SuperscriptBox[RowBox[List["(", RowBox[List["4", "+", RowBox[List["3", " ", "z_"]]]], ")"]], "3"]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["3", RowBox[List["2", "-", RowBox[List["3", " ", "a"]]]]], " ", SqrtBox["\[Pi]"]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["2", "-", RowBox[List["3", " ", "a"]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["5", "2"], "-", RowBox[List["3", " ", "a"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["7", "3"], "-", RowBox[List["4", " ", "a"]]]], ",", "0"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List["2", " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["4", "3"], "-", "a"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["3", " ", "a"]]]], "]"]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["Abs", "[", "z", "]"]], ">", "1"]], "||", RowBox[List[RowBox[List["Re", "[", "z", "]"]], "\[GreaterEqual]", "0"]]]]]]]]]]


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





2001-10-29