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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}={2,2,2,2}





http://functions.wolfram.com/07.34.03.0876.01









  


  








Input Form





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


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





2001-10-29