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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}={1,3,3,3}





http://functions.wolfram.com/07.34.03.0543.01









  


  










Input Form





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