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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}={1,2,2,2}





http://functions.wolfram.com/07.34.03.0412.01









  


  










Input Form





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