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variants of this functions
MeijerG




Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Specific values > Specialized values > Cases with m==3 > Case {m,n,p,q}={3,1,3,3}





http://functions.wolfram.com/07.34.03.1017.01









  


  








Input Form





MeijerG[{{a}, {c, 2 c - a}}, {{b, -1 - b + 2 c, -(1/2) + c}, {}}, z] == ((4^(a - c) Sqrt[Pi] z^(-1 + a) Gamma[1 - a + b] Gamma[-a - b + 2 c])/ Gamma[1 - a + c]^2) Hypergeometric2F1[(1/2) (1 - a + b), (1/2) (-a - b + 2 c), 1 - a + c, -(1/z)]^2








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "a_", "}"]], ",", RowBox[List["{", RowBox[List["c_", ",", RowBox[List[RowBox[List["2", " ", "c_"]], "-", "a_"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["b_", ",", RowBox[List[RowBox[List["-", "1"]], "-", "b_", "+", RowBox[List["2", " ", "c_"]]]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "c_"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["4", RowBox[List["a", "-", "c"]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", "a"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "a", "+", "b"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "a"]], "-", "b", "+", RowBox[List["2", " ", "c"]]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["Hypergeometric2F1", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "a", "+", "b"]], ")"]]]], ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "-", "b", "+", RowBox[List["2", " ", "c"]]]], ")"]]]], ",", RowBox[List["1", "-", "a", "+", "c"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]], "2"]]], SuperscriptBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", "a", "+", "c"]], "]"]], "2"]]]]]]


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





2001-10-29