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/07.34.03.1114.01

 Input Form

 MeijerG[{{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[a, 4]}}, {{Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, {Subscript[b, 4]}}, z] == Pi^2 ((1/Gamma[Subscript[a, 4] - Subscript[b, 1]]) (z^Subscript[b, 1] Csc[Pi (-Subscript[b, 1] + Subscript[b, 2])] Csc[Pi (-Subscript[b, 1] + Subscript[b, 3])] Gamma[1 - Subscript[a, 1] + Subscript[b, 1]] Gamma[1 - Subscript[a, 2] + Subscript[b, 1]] Gamma[1 - Subscript[a, 3] + Subscript[b, 1]] HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 1], 1 - Subscript[a, 2] + Subscript[b, 1], 1 - Subscript[a, 3] + Subscript[b, 1], 1 - Subscript[a, 4] + Subscript[b, 1]}, {1 + Subscript[b, 1] - Subscript[b, 2], 1 + Subscript[b, 1] - Subscript[b, 3], 1 + Subscript[b, 1] - Subscript[b, 4]}, z]) + (1/Gamma[Subscript[a, 4] - Subscript[b, 2]]) (z^Subscript[b, 2] Csc[Pi (Subscript[b, 1] - Subscript[b, 2])] Csc[Pi (-Subscript[b, 2] + Subscript[b, 3])] Gamma[1 - Subscript[a, 1] + Subscript[b, 2]] Gamma[1 - Subscript[a, 2] + Subscript[b, 2]] Gamma[1 - Subscript[a, 3] + Subscript[b, 2]] HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 2], 1 - Subscript[a, 2] + Subscript[b, 2], 1 - Subscript[a, 3] + Subscript[b, 2], 1 - Subscript[a, 4] + Subscript[b, 2]}, {1 - Subscript[b, 1] + Subscript[b, 2], 1 + Subscript[b, 2] - Subscript[b, 3], 1 + Subscript[b, 2] - Subscript[b, 4]}, z]) + (1/Gamma[Subscript[a, 4] - Subscript[b, 3]]) (z^Subscript[b, 3] Csc[Pi (Subscript[b, 1] - Subscript[b, 3])] Csc[Pi (Subscript[b, 2] - Subscript[b, 3])] Gamma[1 - Subscript[a, 1] + Subscript[b, 3]] Gamma[1 - Subscript[a, 2] + Subscript[b, 3]] Gamma[1 - Subscript[a, 3] + Subscript[b, 3]] HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 3], 1 - Subscript[a, 2] + Subscript[b, 3], 1 - Subscript[a, 3] + Subscript[b, 3], 1 - Subscript[a, 4] + Subscript[b, 3]}, {1 - Subscript[b, 1] + Subscript[b, 3], 1 - Subscript[b, 2] + Subscript[b, 3], 1 + Subscript[b, 3] - Subscript[b, 4]}, z])) /; !Element[Subscript[b, 2] - Subscript[b, 1], Integers] && !Element[Subscript[b, 3] - Subscript[b, 1], Integers] && !Element[Subscript[b, 3] - Subscript[b, 2], Integers]

 Standard Form

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 MathML Form

 G 4 , 4 3 , 3 ( z a 1 , a 2 , a 3 , a 4 b 1 , b 2 , b 3 , b 4 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["4", ",", "4"]], RowBox[List["3", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox[SubscriptBox["a", "1"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "4"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "3"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "4"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] π 2 ( 1 Γ ( a 4 - b 1 ) ( z b 1 csc ( π ( b 2 - b 1 ) ) csc ( π ( b 3 - b 1 ) ) Γ ( - a 1 + b 1 + 1 ) Γ ( - a 2 + b 1 + 1 ) Γ ( - a 3 + b 1 + 1 ) 4 F ~ 3 ( - a 1 + b 1 + 1 , - a 2 + b 1 + 1 , - a 3 + b 1 + 1 , - a 4 + b 1 + 1 ; b 1 - b 2 + 1 , b 1 - b 3 + 1 , b 1 - b 4 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "+", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "2"]]], "+", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "3"]]], "+", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "4"]]], "+", SubscriptBox["b", "1"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "3"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "4"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] ) + 1 Γ ( a 4 - b 2 ) ( z b 2 csc ( π ( b 1 - b 2 ) ) csc ( π ( b 3 - b 2 ) ) Γ ( - a 1 + b 2 + 1 ) Γ ( - a 2 + b 2 + 1 ) Γ ( - a 3 + b 2 + 1 ) 4 F ~ 3 ( - a 1 + b 2 + 1 , - a 2 + b 2 + 1 , - a 3 + b 2 + 1 , - a 4 + b 2 + 1 ; - b 1 + b 2 + 1 , b 2 - b 3 + 1 , b 2 - b 4 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "+", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "2"]]], "+", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "3"]]], "+", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "4"]]], "+", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List["-", SubscriptBox["b", "1"]]], "+", SubscriptBox["b", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "2"], "-", SubscriptBox["b", "3"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "2"], "-", SubscriptBox["b", "4"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] ) + 1 Γ ( a 4 - b 3 ) ( z b 3 csc ( π ( b 1 - b 3 ) ) csc ( π ( b 2 - b 3 ) ) Γ ( - a 1 + b 3 + 1 ) Γ ( - a 2 + b 3 + 1 ) Γ ( - a 3 + b 3 + 1 ) 4 F ~ 3 ( - a 1 + b 3 + 1 , - a 2 + b 3 + 1 , - a 3 + b 3 + 1 , - a 4 + b 3 + 1 ; - b 1 + b 3 + 1 , - b 2 + b 3 + 1 , b 3 - b 4 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "+", SubscriptBox["b", "3"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "2"]]], "+", SubscriptBox["b", "3"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "3"]]], "+", SubscriptBox["b", "3"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["a", "4"]]], "+", SubscriptBox["b", "3"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[RowBox[List["-", SubscriptBox["b", "1"]]], "+", SubscriptBox["b", "3"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["-", SubscriptBox["b", "2"]]], "+", SubscriptBox["b", "3"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "3"], "-", SubscriptBox["b", "4"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] ) ) /; b 2 - b 1 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] b 3 - b 1 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] b 3 - b 2 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition MeijerG Subscript a 1 Subscript a 2 Subscript a 3 Subscript a 4 Subscript b 1 Subscript b 2 Subscript b 3 Subscript b 4 z 2 1 Gamma Subscript a 4 -1 Subscript b 1 -1 z Subscript b 1 Subscript b 2 -1 Subscript b 1 Subscript b 3 -1 Subscript b 1 Gamma -1 Subscript a 1 Subscript b 1 1 Gamma -1 Subscript a 2 Subscript b 1 1 Gamma -1 Subscript a 3 Subscript b 1 1 HypergeometricPFQRegularized -1 Subscript a 1 Subscript b 1 1 -1 Subscript a 2 Subscript b 1 1 -1 Subscript a 3 Subscript b 1 1 -1 Subscript a 4 Subscript b 1 1 Subscript b 1 -1 Subscript b 2 1 Subscript b 1 -1 Subscript b 3 1 Subscript b 1 -1 Subscript b 4 1 z 1 Gamma Subscript a 4 -1 Subscript b 2 -1 z Subscript b 2 Subscript b 1 -1 Subscript b 2 Subscript b 3 -1 Subscript b 2 Gamma -1 Subscript a 1 Subscript b 2 1 Gamma -1 Subscript a 2 Subscript b 2 1 Gamma -1 Subscript a 3 Subscript b 2 1 HypergeometricPFQRegularized -1 Subscript a 1 Subscript b 2 1 -1 Subscript a 2 Subscript b 2 1 -1 Subscript a 3 Subscript b 2 1 -1 Subscript a 4 Subscript b 2 1 -1 Subscript b 1 Subscript b 2 1 Subscript b 2 -1 Subscript b 3 1 Subscript b 2 -1 Subscript b 4 1 z 1 Gamma Subscript a 4 -1 Subscript b 3 -1 z Subscript b 3 Subscript b 1 -1 Subscript b 3 Subscript b 2 -1 Subscript b 3 Gamma -1 Subscript a 1 Subscript b 3 1 Gamma -1 Subscript a 2 Subscript b 3 1 Gamma -1 Subscript a 3 Subscript b 3 1 HypergeometricPFQRegularized -1 Subscript a 1 Subscript b 3 1 -1 Subscript a 2 Subscript b 3 1 -1 Subscript a 3 Subscript b 3 1 -1 Subscript a 4 Subscript b 3 1 -1 Subscript b 1 Subscript b 3 1 -1 Subscript b 2 Subscript b 3 1 Subscript b 3 -1 Subscript b 4 1 z Subscript b 2 -1 Subscript b 1 Subscript b 3 -1 Subscript b 1 Subscript b 3 -1 Subscript b 2 [/itex]

 Rule Form

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

 2007-05-02