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 MeijerG

 http://functions.wolfram.com/07.34.03.1028.01

 Input Form

 MeijerG[{{a}, {c, 2 c - a + 2}}, {{b, 1 - b + 2 c, 1/2 + c}, {}}, z] == (-((2^(2 (-1 + a - c)) Sqrt[Pi] Gamma[1 - a + b] Gamma[2 - a - b + 2 c])/ ((1 - a + c) Gamma[1 - a + c]^2))) z^(-1 + a) Hypergeometric2F1[(b - a + 1)/2, Hypergeometric2F1[c + 1 - (a + b)/2], 2 - a + c, -(1/z)] (-2 Hypergeometric2F1[(b - a + 1)/2, Hypergeometric2F1[c + 1 - (a + b)/2], 1 - a + c, -(1/z)] + Hypergeometric2F1[(b - a + 1)/2, Hypergeometric2F1[c + 1 - (a + b)/2], 2 - a + c, -(1/z)])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "a", "}"]], ",", RowBox[List["{", RowBox[List["c", ",", RowBox[List[RowBox[List["2", " ", "c"]], "-", "a", "+", "2"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["b", ",", RowBox[List["1", "-", "b", "+", RowBox[List["2", " ", "c"]]]], ",", RowBox[List[FractionBox["1", "2"], "+", "c"]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "a", "-", "c"]], ")"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "a", "+", "b"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["2", "-", "a", "-", "b", "+", RowBox[List["2", " ", "c"]]]], "]"]], " "]], RowBox[List[RowBox[List["(", RowBox[List["1", "-", "a", "+", "c"]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", RowBox[List["1", "-", "a", "+", "c"]], "]"]], "2"]]]]]], SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", "a"]]], RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["b", "-", "a", "+", "1"]], "2"], ",", TagBox[RowBox[List["c", "+", "1", "-", FractionBox[RowBox[List["a", "+", "b"]], "2"]]], Hypergeometric2F1, Rule[Editable, True]], ",", RowBox[List["2", "-", "a", "+", "c"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["b", "-", "a", "+", "1"]], "2"], ",", TagBox[RowBox[List["c", "+", "1", "-", FractionBox[RowBox[List["a", "+", "b"]], "2"]]], Hypergeometric2F1, Rule[Editable, True]], ",", RowBox[List["1", "-", "a", "+", "c"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]]]], "+", RowBox[List["Hypergeometric2F1", "[", RowBox[List[FractionBox[RowBox[List["b", "-", "a", "+", "1"]], "2"], ",", TagBox[RowBox[List["c", "+", "1", "-", FractionBox[RowBox[List["a", "+", "b"]], "2"]]], Hypergeometric2F1, Rule[Editable, True]], ",", RowBox[List["2", "-", "a", "+", "c"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]]]], ")"]]]]]]]]

 MathML Form

 G 3 , 3 3 , 1 ( z a , c , 2 c - a + 2 b , 2 c - b + 1 , c + 1 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "3"]], RowBox[List["3", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["a", MeijerG, Rule[Editable, True]], ",", TagBox["c", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["2", " ", "c"]], "-", "a", "+", "2"]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["b", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["2", " ", "c"]], "-", "b", "+", "1"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["c", "+", FractionBox["1", "2"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] - 2 2 ( a - c - 1 ) π Γ ( b - a + 1 ) Γ ( 2 c - a - b + 2 ) ( c - a + 1 ) Γ ( c - a + 1 ) 2 z a - 1 2 F 1 ( b - a + 1 2 , c + 1 - a + b 2 ; c - a + 2 ; - 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["b", "-", "a", "+", "1"]], "2"], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["c", "+", "1", "-", FractionBox[RowBox[List["a", "+", "b"]], "2"]]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["c", "-", "a", "+", "2"]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "z"]]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] ( 2 F 1 ( b - a + 1 2 , c + 1 - a + b 2 ; c - a + 2 ; - 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["b", "-", "a", "+", "1"]], "2"], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[TagBox[RowBox[List["c", "+", "1", "-", FractionBox[RowBox[List["a", "+", "b"]], "2"]]], Hypergeometric2F1, Rule[Editable, True]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["c", "-", "a", "+", "2"]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "z"]]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] - 2 2 F 1 ( b - a + 1 2 , c + 1 - a + b 2 ; c - a + 1 ; - 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["b", "-", "a", "+", "1"]], "2"], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["c", "+", "1", "-", FractionBox[RowBox[List["a", "+", "b"]], "2"]]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["c", "-", "a", "+", "1"]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "z"]]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] ) MeijerG a c 2 c -1 a 2 b 2 c -1 b 1 c 1 2 z -1 2 2 a -1 c -1 1 2 Gamma b -1 a 1 Gamma 2 c -1 a -1 b 2 c -1 a 1 Gamma c -1 a 1 2 -1 z a -1 Hypergeometric2F1 b -1 a 1 2 -1 c 1 -1 a b 2 -1 c -1 a 2 -1 1 z -1 Hypergeometric2F1 b -1 a 1 2 -1 Hypergeometric2F1 c 1 -1 a b 2 -1 c -1 a 2 -1 1 z -1 -1 2 Hypergeometric2F1 b -1 a 1 2 -1 c 1 -1 a b 2 -1 c -1 a 1 -1 1 z -1 [/itex]

 Rule Form

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

 2001-10-29