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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}={2,2,3,3}





http://functions.wolfram.com/07.34.03.0903.01









  


  








Input Form





MeijerG[{{a, c}, {2 a - c}}, {{b, -(1/2) + a}, {-1 + 2 a - b}}, z] == Sqrt[2] Pi z^(-(3/4) + a) Gamma[1 + b - c] LegendreP[-1 + a - b, -a + c, 3, Sqrt[1 + 1/z]] LegendreP[-(1/2) - a + c, -(1/2) + a - b, 3, Sqrt[1 + 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_", ",", "c_"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", " ", "a_"]], "-", "c_"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["b_", ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "a_"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "a_"]], "-", "b_"]], "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox["2"], " ", "\[Pi]", " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", FractionBox["3", "4"]]], "+", "a"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "b", "-", "c"]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "a", "-", "b"]], ",", RowBox[List[RowBox[List["-", "a"]], "+", "c"]], ",", "3", ",", SqrtBox[RowBox[List["1", "+", FractionBox["1", "z"]]]]]], "]"]], " ", RowBox[List["LegendreP", "[", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "a", "+", "c"]], ",", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "a", "-", "b"]], ",", "3", ",", SqrtBox[RowBox[List["1", "+", "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