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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==1 > Case {m,n,p,q}={1,1,2,2}





http://functions.wolfram.com/07.34.03.0340.01









  


  








Input Form





MeijerG[{{a}, {a + 1/2}}, {{b}, {b - 1/2}}, z] == (Gamma[-a + b]/(Sqrt[Pi] Gamma[a - b + 1/2])) z^(b - 1/2) (Sign[1 - Abs[z]] (1 - z))^(a - b) Sinh[(b - a) ArcTanh[(2 Sqrt[z])/(z + 1)]] /; !IntervalMemberQ[Interval[{-1, 0}], z]








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["a_", "+", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "b_", "}"]], ",", RowBox[List["{", RowBox[List["b_", "-", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], "]"]], " ", SuperscriptBox["z", RowBox[List["b", "-", FractionBox["1", "2"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["Sign", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z", "]"]]]], "]"]], " ", RowBox[List["(", RowBox[List["1", "-", "z"]], ")"]]]], ")"]], RowBox[List["a", "-", "b"]]], " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "a"]], ")"]], " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List["2", " ", SqrtBox["z"]]], RowBox[List["z", "+", "1"]]], "]"]]]], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["a", "-", "b", "+", FractionBox["1", "2"]]], "]"]]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29