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/07.34.03.1007.01

 Input Form

 MeijerG[{{a}, {c, 2 b - c + 1}}, {{b, (1/2) (-1 + a + c), (1/2) (a - c) + b}, {}}, z] == ((2 Pi Gamma[1 - a + b])/(Gamma[b + (1/2) (3 - a - c)] Gamma[1 + (1/2) (-a + c)])) z^b (1 + 4 z)^(-1 + a - b) HypergeometricPFQ[{(1 - a + b)/3, (2 - a + b)/3, 1 + (b - a)/3}, {(3 - a - c)/2 + b, 1 + (c - a)/2}, (27 z)/(1 + 4 z)^3]

 Standard Form

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 MathML Form

 G 3 , 3 3 , 1 ( z a , c , 2 b - c + 1 b , a + c - 1 2 , b + a - c 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", " ", "b"]], "-", "c", "+", "1"]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["b", MeijerG, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["a", "+", "c", "-", "1"]], "2"], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["b", "+", FractionBox[RowBox[List["a", "-", "c"]], "2"]]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] 2 π Γ ( b - a + 1 ) Γ ( b + 3 - a - c 2 ) Γ ( c - a 2 + 1 ) z b ( 4 z + 1 ) a - b - 1 3 F 2 ( 1 - a + b 3 , 2 - a + b 3 , b - a 3 + 1 ; b + 3 - a - c 2 , c - a 2 + 1 ; 27 z ( 4 z + 1 ) 3 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["1", "-", "a", "+", "b"]], "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox[RowBox[List["2", "-", "a", "+", "b"]], "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["b", "-", "a"]], "3"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["b", "+", FractionBox[RowBox[List["3", "-", "a", "-", "c"]], "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["c", "-", "a"]], "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox[RowBox[List["27", " ", "z"]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["4", " ", "z"]], "+", "1"]], ")"]], "3"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] MeijerG a c 2 b -1 c 1 b a c -1 2 -1 b a -1 c 2 -1 z 2 Gamma b -1 a 1 Gamma b 3 -1 a -1 c 2 -1 Gamma c -1 a 2 -1 1 -1 z b 4 z 1 a -1 b -1 HypergeometricPFQ 1 -1 a b 3 -1 2 -1 a b 3 -1 b -1 a 3 -1 1 b 3 -1 a -1 c 2 -1 c -1 a 2 -1 1 27 z 4 z 1 3 -1 [/itex]

 Rule Form

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

 2001-10-29