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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}={0,3,4,0}





http://functions.wolfram.com/07.34.03.0209.01









  


  








Input Form





MeijerG[{{a, c, 2 a - c}, {a - 1/2}}, {{}, {}}, z] == 2 Sqrt[Pi] Csc[(a - c) Pi] z^(-1 + a) (-BesselJ[2 a - 2 c, (2 Sqrt[2])/z^(1/4)] + BesselJ[-2 a + 2 c, (2 Sqrt[2])/z^(1/4)]) BesselK[2 a - 2 c, (2 Sqrt[2])/z^(1/4)] /; !IntervalMemberQ[Interval[{-Infinity, 0}], z]








Standard Form





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MathML Form







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</mi> </mrow> <mo> , </mo> <mn> 0 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </annotation-xml> </semantics> </math>










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["2", " ", "a_"]], "-", "c_"]]]], "}"]], ",", RowBox[List["{", RowBox[List["a_", "-", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Csc", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "c"]], ")"]], " ", "\[Pi]"]], "]"]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", "a"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List[RowBox[List["2", " ", "a"]], "-", RowBox[List["2", " ", "c"]]]], ",", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], "]"]]]], "+", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", "c"]]]], ",", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], "]"]]]], ")"]], " ", RowBox[List["BesselK", "[", RowBox[List[RowBox[List[RowBox[List["2", " ", "a"]], "-", RowBox[List["2", " ", "c"]]]], ",", FractionBox[RowBox[List["2", " ", SqrtBox["2"]]], SuperscriptBox["z", RowBox[List["1", "/", "4"]]]]]], "]"]]]], "/;", 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