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 MeijerG

 http://functions.wolfram.com/07.34.03.1008.01

 Input Form

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

 Standard Form

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 MathML Form

 G 3 , 3 3 , 1 ( z a , c , 2 c - a - 1 b , 2 c - b - 2 , 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", "-", "1"]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["b", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["2", " ", "c"]], "-", "b", "-", "2"]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["c", "-", FractionBox["1", "2"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] - 2 2 ( a - c ) π z a - 1 Γ ( b - a + 1 ) Γ ( 2 c - a - b - 1 ) ( a - c ) ( c - b - 1 ) Γ ( c - a ) 2 ( ( a - b - 1 ) 2 F 1 ( b - a 2 + 1 , c - a + b + 1 2 ; c - a ; - 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[RowBox[List[FractionBox[RowBox[List["b", "-", "a"]], "2"], " ", "+", "1"]], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["c", "-", FractionBox[RowBox[List["a", "+", "b", "+", "1"]], "2"]]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["c", "-", "a"]], 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 2 + 1 , c - a + b + 1 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[TagBox[RowBox[List[FractionBox[RowBox[List["b", "-", "a"]], "2"], " ", "+", "1"]], Hypergeometric2F1, Rule[Editable, True]], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["c", "-", FractionBox[RowBox[List["a", "+", "b", "+", "1"]], "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] - ( a + b - 2 c + 1 ) 2 F 1 ( b - a + 1 2 , c - a + b 2 ; c - a ; - 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", "-", 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"]], 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 - 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", "-", 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 -1 b 2 c -1 b -2 c -1 1 2 z -1 2 2 a -1 c 1 2 z a -1 Gamma b -1 a 1 Gamma 2 c -1 a -1 b -1 a -1 c c -1 b -1 Gamma c -1 a 2 -1 a -1 b -1 Hypergeometric2F1 b -1 a 2 -1 1 c -1 a b 1 2 -1 c -1 a -1 1 z -1 Hypergeometric2F1 Hypergeometric2F1 b -1 a 2 -1 1 c -1 a b 1 2 -1 c -1 a 1 -1 1 z -1 -1 a b -1 2 c 1 Hypergeometric2F1 b -1 a 1 2 -1 c -1 a b 2 -1 c -1 a -1 1 z -1 Hypergeometric2F1 b -1 a 1 2 -1 c -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