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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==0 > Case {m,n,p,q}={0,2,2,2}





http://functions.wolfram.com/07.34.03.0110.01









  


  








Input Form





MeijerG[{{a, c}, {}}, {{}, {b, (1/2) (-1 + a + c)}}, z] == (UnitStep[-1 + Abs[z]]/(E^((1/2) I (a - c) Pi) (Sqrt[Pi] Gamma[a - b]))) (-1 + z)^((1/4) (-2 + a - 2 b + c)) z^((1/4) (-2 + a + 2 b + c)) LegendreQ[(a + c)/2 - b - 1, (a - c)/2, 3, (-1 + 2 z)/(2 Sqrt[-1 + z] Sqrt[z])] /; 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["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["a_", ",", "c_"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List["b_", ",", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a_", "+", "c_"]], ")"]]]]]], "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["a", "-", "c"]], ")"]], " ", "\[Pi]"]]], " ", RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Abs", "[", "z", "]"]]]], "]"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "z"]], ")"]], RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "a", "-", RowBox[List["2", " ", "b"]], "+", "c"]], ")"]]]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "a", "+", RowBox[List["2", " ", "b"]], "+", "c"]], ")"]]]]], " ", RowBox[List["LegendreQ", "[", RowBox[List[RowBox[List[FractionBox[RowBox[List["a", "+", "c"]], "2"], "-", "b", "-", "1"]], ",", FractionBox[RowBox[List["a", "-", "c"]], "2"], ",", "3", ",", FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "1"]], "+", "z"]]], " ", SqrtBox["z"]]]]]], "]"]]]], RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["a", "-", "b"]], "]"]]]]], "/;", RowBox[List[RowBox[List["Re", "[", "z", "]"]], ">", "0"]]]]]]]]


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





2001-10-29