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 MeijerG

 http://functions.wolfram.com/07.34.03.0594.01

 Input Form

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

 Standard Form

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 MathML Form

 G 4 , 4 1 , 4 ( z a , c , d , a - c + d b , a + d - 1 2 , a + d 2 , a - b + d - 1 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "4"]], RowBox[List["1", ",", "4"]]], "\[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["d", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "-", "c", "+", "d"]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["b", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["a", "+", "d", "-", "1"]], "2"], MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["a", "+", "d"]], "2"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "-", "b", "+", "d", "-", "1"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] Γ ( b - a + 1 ) Γ ( b - c + 1 ) Γ ( b - d + 1 ) Γ ( b - a + c - d + 1 ) Γ ( 2 b - a - d + 2 ) Γ ( b + 3 - a - d 2 ) Γ ( b - a + d 2 + 1 ) z b ( 2 z - 2 - z - 1 - z + 1 ) b - a + 1 2 F 1 ( b - a + 1 , b - c + 1 ; 2 b - a - d + 2 ; 2 - z - 1 - z - 2 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["b", "-", "a", "+", "1"]], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["b", "-", "c", "+", "1"]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[RowBox[List["2", " ", "b"]], "-", "a", "-", "d", "+", "2"]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List[RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "z"]], "-", "1"]]], " ", SqrtBox[RowBox[List["-", "z"]]]]], "-", RowBox[List["2", " ", "z"]]]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] 2 F 1 ( b - a + 1 , b + c - a - d + 1 ; 2 b - a - d + 2 ; 2 - z - 1 - z - 2 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["b", "-", "a", "+", "1"]], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List["b", "+", "c", "-", "a", "-", "d", "+", "1"]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[RowBox[List["2", " ", "b"]], "-", "a", "-", "d", "+", "2"]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List[RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "z"]], "-", "1"]]], " ", SqrtBox[RowBox[List["-", "z"]]]]], "-", RowBox[List["2", " ", "z"]]]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] MeijerG a c d a -1 c d b a d -1 2 -1 a d 2 -1 a -1 b d -1 z Gamma b -1 a 1 Gamma b -1 c 1 Gamma b -1 d 1 Gamma b -1 a c -1 d 1 Gamma 2 b -1 a -1 d 2 Gamma b 3 -1 a -1 d 2 -1 Gamma b -1 a d 2 -1 1 -1 z b 2 z -1 2 -1 z -1 1 2 -1 z 1 2 1 b -1 a 1 Hypergeometric2F1 b -1 a 1 b -1 c 1 2 b -1 a -1 d 2 2 -1 z -1 1 2 -1 z 1 2 -1 2 z Hypergeometric2F1 b -1 a 1 b c -1 a -1 d 1 2 b -1 a -1 d 2 2 -1 z -1 1 2 -1 z 1 2 -1 2 z [/itex]

 Rule Form

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

 2001-10-29