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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==2 > Case {m,n,p,q}={2,2,5,3}





http://functions.wolfram.com/07.34.03.0934.01









  


  








Input Form





MeijerG[{{a, 1/2 + a}, {c, 1 - a + 2 b, 1/2 - a + 2 b}}, {{b, 1/2 + b}, {c}}, z] == Sqrt[2] z^(-(1/4) + b) Cos[(a - c) Pi + 1/Sqrt[z]] BesselJ[1/2 - 2 a + 2 b, 1/Sqrt[z]] /; !IntervalMemberQ[Interval[{-Infinity, 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["{", RowBox[List["a_", ",", RowBox[List[FractionBox["1", "2"], "+", "a_"]]]], "}"]], ",", RowBox[List["{", RowBox[List["c_", ",", RowBox[List["1", "-", "a_", "+", RowBox[List["2", " ", "b_"]]]], ",", RowBox[List[FractionBox["1", "2"], "-", "a_", "+", RowBox[List["2", " ", "b_"]]]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["b_", ",", RowBox[List[FractionBox["1", "2"], "+", "b_"]]]], "}"]], ",", RowBox[List["{", "c_", "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox["2"], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], "+", "b"]]], " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "c"]], ")"]], " ", "\[Pi]"]], "+", FractionBox["1", SqrtBox["z"]]]], "]"]], " ", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List[FractionBox["1", "2"], "-", RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]], ",", FractionBox["1", SqrtBox["z"]]]], "]"]]]], "/;", RowBox[List["!", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]]]]]]]]]]


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





2001-10-29