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/07.34.03.0204.01

 Input Form

 MeijerG[{{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {}}, {{}, {Subscript[b, 1], Subscript[b, 2]}}, z] == Pi^2 (((Csc[Pi (Subscript[a, 1] - Subscript[a, 2])] Csc[Pi (Subscript[a, 1] - Subscript[a, 3])])/ (Gamma[Subscript[a, 1] - Subscript[b, 1]] Gamma[Subscript[a, 1] - Subscript[b, 2]])) z^(-1 + Subscript[a, 1]) HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 1], 1 - Subscript[a, 1] + Subscript[b, 2]}, {1 - Subscript[a, 1] + Subscript[a, 2], 1 - Subscript[a, 1] + Subscript[a, 3]}, -(1/z)] + ((Csc[Pi (-Subscript[a, 1] + Subscript[a, 2])] Csc[Pi (Subscript[a, 2] - Subscript[a, 3])])/ (Gamma[Subscript[a, 2] - Subscript[b, 1]] Gamma[Subscript[a, 2] - Subscript[b, 2]])) z^(-1 + Subscript[a, 2]) HypergeometricPFQRegularized[{1 - Subscript[a, 2] + Subscript[b, 1], 1 - Subscript[a, 2] + Subscript[b, 2]}, {1 + Subscript[a, 1] - Subscript[a, 2], 1 - Subscript[a, 2] + Subscript[a, 3]}, -(1/z)] + ((Csc[Pi (-Subscript[a, 1] + Subscript[a, 3])] Csc[Pi (-Subscript[a, 2] + Subscript[a, 3])])/ (Gamma[Subscript[a, 3] - Subscript[b, 1]] Gamma[Subscript[a, 3] - Subscript[b, 2]])) z^(-1 + Subscript[a, 3]) HypergeometricPFQRegularized[{1 - Subscript[a, 3] + Subscript[b, 1], 1 - Subscript[a, 3] + Subscript[b, 2]}, {1 + Subscript[a, 1] - Subscript[a, 3], 1 + Subscript[a, 2] - Subscript[a, 3]}, -(1/z)]) /; !IntervalMemberQ[Interval[{-Infinity, 0}], z] && !Element[Subscript[a, 2] - Subscript[a, 1], Integers] && !Element[Subscript[a, 3] - Subscript[a, 1], Integers] && !Element[Subscript[a, 3] - Subscript[a, 2], Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["a", "1"], ",", SubscriptBox["a", "2"], ",", SubscriptBox["a", "3"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"]]], "}"]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[SuperscriptBox["\[Pi]", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["a", "2"]]], ")"]]]], "]"]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["a", "3"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["b", "1"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["b", "2"]]], "]"]]]]], " ", SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["a", "1"]]]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["a", "3"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "+", SubscriptBox["a", "2"]]], ")"]]]], "]"]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["a", "3"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["b", "1"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["b", "2"]]], "]"]]]]], SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["a", "2"]]]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "2"], "+", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"], "+", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["a", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"], "+", SubscriptBox["a", "3"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List[RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["a", "1"]]], "+", SubscriptBox["a", "3"]]], ")"]]]], "]"]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["a", "2"]]], "+", SubscriptBox["a", "3"]]], ")"]]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "3"], "-", SubscriptBox["b", "1"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "3"], "-", SubscriptBox["b", "2"]]], "]"]]]]], SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["a", "3"]]]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "3"], "+", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "3"], "+", SubscriptBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["a", "1"], "-", SubscriptBox["a", "3"]]], ",", RowBox[List["1", "+", SubscriptBox["a", "2"], "-", SubscriptBox["a", "3"]]]]], "}"]], ",", RowBox[List["-", FractionBox["1", "z"]]]]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["Not", "[", RowBox[List["IntervalMemberQ", "[", RowBox[List[RowBox[List["Interval", "[", RowBox[List["{", RowBox[List[RowBox[List["-", "\[Infinity]"]], ",", "0"]], "}"]], "]"]], ",", "z"]], "]"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["a", "1"]]], ",", "Integers"]], "]"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[RowBox[List[SubscriptBox["a", "3"], "-", SubscriptBox["a", "1"]]], ",", "Integers"]], "]"]], "]"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List[RowBox[List[SubscriptBox["a", "3"], "-", SubscriptBox["a", "2"]]], ",", "Integers"]], "]"]], "]"]]]]]]]]

 MathML Form

 G 3 , 2 0 , 3 ( z a 1 , a 2 , a 3 b 1 , b 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "2"]], RowBox[List["0", ",", "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]]]]], List[RowBox[List[TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] π 2 ( csc ( π ( a 1 - a 2 ) ) csc ( π ( a 1 - a 3 ) ) Γ ( a 1 - b 1 ) Γ ( a 1 - b 2 ) z a 1 - 1 2 F ~ 2 ( 1 - a 1 + b 1 , 1 - a 1 + b 2 ; 1 - a 1 + a 2 , 1 - a 1 + a 3 ; - 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["b", "1"]]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["b", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["a", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["a", "3"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "z"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] + csc ( π ( a 2 - a 1 ) ) csc ( π ( a 2 - a 3 ) ) Γ ( a 2 - b 1 ) Γ ( a 2 - b 2 ) z a 2 - 1 2 F ~ 2 ( 1 - a 2 + b 1 , 1 - a 2 + b 2 ; a 1 - a 2 + 1 , 1 - a 2 + a 3 ; - 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"], "+", SubscriptBox["b", "1"]]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"], "+", SubscriptBox["b", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["a", "2"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"], "+", SubscriptBox["a", "3"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "z"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] + csc ( π ( a 3 - a 1 ) ) csc ( π ( a 3 - a 2 ) ) Γ ( a 3 - b 1 ) Γ ( a 3 - b 2 ) z a 3 - 1 2 F ~ 2 ( 1 - a 3 + b 1 , 1 - a 3 + b 2 ; a 1 - a 3 + 1 , a 2 - a 3 + 1 ; - 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "3"], "+", SubscriptBox["b", "1"]]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "3"], "+", SubscriptBox["b", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[SubscriptBox["a", "1"], "-", SubscriptBox["a", "3"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["a", "3"], "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["1", "z"]]], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] ) /; z ( - , 0 ) a 2 - a 1 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] a 3 - a 1 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] a 3 - a 2 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] G 3 , 2 0 , 3 ( z a 1 , a 2 , a 3 b 1 , b 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "2"]], RowBox[List["0", ",", "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]]]]], List[RowBox[List[TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] π 2 ( csc ( π ( a 1 - a 2 ) ) csc ( π ( a 1 - a 3 ) ) Γ ( a 1 - b 1 ) Γ ( a 1 - b 2 ) z a 1 - 1 2 F ~ 2 ( 1 - a 1 + b 1 , 1 - a 1 + b 2 ; 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z ( - , 0 ) a 2 - a 1 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] a 3 - a 1 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] a 3 - a 2 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] [/itex]

 Rule Form

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

 2001-10-29