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; }

 HypergeometricPFQ

 http://functions.wolfram.com/07.27.13.0014.01

 Input Form

 Wronskian[s^z HypergeometricPFQRegularized[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, a r^z], s^z (MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, 1 - Subscript[b, 1]}, {1 - Subscript[b, 2]}}, a r^z] + MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, 1 - Subscript[b, 2]}, {1 - Subscript[b, 1]}}, a r^z]), s^z MeijerG[{{1 - Subscript[a, 1], 1 - Subscript[a, 2], 1 - Subscript[a, 3]}, {}}, {{0, 1 - Subscript[b, 1], 1 - Subscript[b, 2]}, {}}, (-a) r^z], z] == a^3 r^(3 z) ((-a) r^z)^(-Subscript[b, 1] - Subscript[b, 2]) (a r^z)^(-1 - Subscript[b, 1] - Subscript[b, 2]) (1 - a r^z)^(-2 - Subscript[a, 1] - Subscript[a, 2] - Subscript[a, 3] + Subscript[b, 1] + Subscript[b, 2]) (((-a) r^z)^Subscript[b, 2] (a r^z)^Subscript[b, 1] + ((-a) r^z)^Subscript[b, 1] (a r^z)^Subscript[b, 2]) s^(3 z) Gamma[1 + Subscript[a, 1] - Subscript[b, 1]] Gamma[1 + Subscript[a, 2] - Subscript[b, 1]] Gamma[1 + Subscript[a, 3] - Subscript[b, 1]] Gamma[1 + Subscript[a, 1] - Subscript[b, 2]] Gamma[1 + Subscript[a, 2] - Subscript[b, 2]] Gamma[1 + Subscript[a, 3] - Subscript[b, 2]] Log[r]^3

 Standard Form

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 MathML Form

 W z ( s z 3 F ~ 2 ( a 1 , a 2 , a 3 ; b 1 , b 2 ; a r z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "3"], SubscriptBox[OverscriptBox["F", "~"], "2"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[SubscriptBox["b", "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["a", " ", SuperscriptBox["r", "z"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQRegularized] , s z ( G 3 , 3 2 , 3 ( a r z 1 - a 1 , 1 - a 2 , 1 - a 3 0 , 1 - b 1 , 1 - b 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "3"]], RowBox[List["2", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["a", " ", SuperscriptBox["r", "z"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "3"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] + G 3 , 3 2 , 3 ( a r z 1 - a 1 , 1 - a 2 , 1 - a 3 0 , 1 - b 2 , 1 - b 1 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "3"]], RowBox[List["2", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List["a", " ", SuperscriptBox["r", "z"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "3"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] ) , s z G 3 , 3 3 , 3 ( - a r z 1 - a 1 , 1 - a 2 , 1 - a 3 0 , 1 - b 1 , 1 - b 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "3"]], RowBox[List["3", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["r", "z"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "3"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "1"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], MeijerG, Rule[Editable, True], Rule[Selectable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False], Rule[Selectable, False]] ) a 3 r 3 z ( - a r z ) - b 1 - b 2 ( a r z ) - b 1 - b 2 - 1 ( 1 - a r z ) - a 1 - a 2 - a 3 + b 1 + b 2 - 2 ( ( a r z ) b 2 ( - a r z ) b 1 + ( a r z ) b 1 ( - a r z ) b 2 ) s 3 z Γ ( a 1 - b 1 + 1 ) Γ ( a 2 - b 1 + 1 ) Γ ( a 3 - b 1 + 1 ) Γ ( a 1 - b 2 + 1 ) Γ ( a 2 - b 2 + 1 ) Γ ( a 3 - b 2 + 1 ) log 3 ( r ) Subscript W z s z HypergeometricPFQRegularized Subscript a 1 Subscript a 2 Subscript a 3 Subscript b 1 Subscript b 2 a r z s z MeijerG 1 -1 Subscript a 1 1 -1 Subscript a 2 1 -1 Subscript a 3 0 1 -1 Subscript b 1 1 -1 Subscript b 2 a r z MeijerG 1 -1 Subscript a 1 1 -1 Subscript a 2 1 -1 Subscript a 3 0 1 -1 Subscript b 2 1 -1 Subscript b 1 a r z s z MeijerG 1 -1 Subscript a 1 1 -1 Subscript a 2 1 -1 Subscript a 3 0 1 -1 Subscript b 1 1 -1 Subscript b 2 -1 a r z a 3 r 3 z -1 a r z -1 Subscript b 1 -1 Subscript b 2 a r z -1 Subscript b 1 -1 Subscript b 2 -1 1 -1 a r z -1 Subscript a 1 -1 Subscript a 2 -1 Subscript a 3 Subscript b 1 Subscript b 2 -2 a r z Subscript b 2 -1 a r z Subscript b 1 a r z Subscript b 1 -1 a r z Subscript b 2 s 3 z Gamma Subscript a 1 -1 Subscript b 1 1 Gamma Subscript a 2 -1 Subscript b 1 1 Gamma Subscript a 3 -1 Subscript b 1 1 Gamma Subscript a 1 -1 Subscript b 2 1 Gamma Subscript a 2 -1 Subscript b 2 1 Gamma Subscript a 3 -1 Subscript b 2 1 r 3 [/itex]

 Rule Form

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

 2007-05-02