html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 MeijerG

 http://functions.wolfram.com/07.34.03.1071.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29