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/07.34.03.0516.01

 Input Form

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

 Standard Form

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 MathML Form

 G 3 , 3 1 , 2 ( z a 1 , a 2 , a 3 b 1 , b 2 , b 3 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "3"]], RowBox[List["1", ",", "2"]]], "\[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]], ",", TagBox[SubscriptBox["b", "3"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] csc ( π ( a 1 - a 2 ) ) π ( sin ( π ( a 1 - b 2 ) ) sin ( π ( a 1 - b 3 ) ) Γ ( 1 - a 1 + b 1 ) Γ ( 1 - a 1 + b 2 ) Γ ( 1 - a 1 + b 3 ) z a 1 - 1 3 F ~ 2 ( 1 - a 1 + b 1 , 1 - a 1 + b 2 , 1 - a 1 + b 3 ; 1 - a 1 + a 2 , 1 - a 1 + a 3 ; 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", 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]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["b", "3"]]], 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[FractionBox["1", "z"], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] - sin ( π ( a 2 - b 2 ) ) sin ( π ( a 2 - b 3 ) ) Γ ( 1 - a 2 + b 1 ) Γ ( 1 - a 2 + b 2 ) Γ ( 1 - a 2 + b 3 ) z a 2 - 1 3 F ~ 2 ( 1 - a 2 + b 1 , 1 - a 2 + b 2 , 1 - a 2 + b 3 ; a 1 - a 2 + 1 , 1 - a 2 + a 3 ; 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", 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]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"], "+", SubscriptBox["b", "3"]]], 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[FractionBox["1", "z"], HypergeometricPFQRegularized, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQRegularized] ) θ UnitStep ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" - 1 ) + sin ( π ( a 3 - b 1 ) ) π Γ ( 1 - a 1 + b 1 ) Γ ( 1 - a 2 + b 1 ) Γ ( 1 - a 3 + b 1 ) z b 1 3 F ~ 2 ( 1 - a 1 + b 1 , 1 - a 2 + b 1 , 1 - a 3 + b 1 ; b 1 - b 2 + 1 , b 1 - b 3 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", 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", "2"], "+", SubscriptBox["b", "1"]]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "3"], "+", SubscriptBox["b", "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]]]], 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] θ UnitStep ( 1 - "\[LeftBracketingBar]" z "\[RightBracketingBar]" ) /; a 2 - a 1 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition MeijerG Subscript a 1 Subscript a 2 Subscript a 3 Subscript b 1 Subscript b 2 Subscript b 3 z Subscript a 1 -1 Subscript a 2 -1 Subscript a 1 -1 Subscript b 2 Subscript a 1 -1 Subscript b 3 Gamma 1 -1 Subscript a 1 Subscript b 1 Gamma 1 -1 Subscript a 1 Subscript b 2 Gamma 1 -1 Subscript a 1 Subscript b 3 z Subscript a 1 -1 HypergeometricPFQRegularized 1 -1 Subscript a 1 Subscript b 1 1 -1 Subscript a 1 Subscript b 2 1 -1 Subscript a 1 Subscript b 3 1 -1 Subscript a 1 Subscript a 2 1 -1 Subscript a 1 Subscript a 3 1 z -1 -1 Subscript a 2 -1 Subscript b 2 Subscript a 2 -1 Subscript b 3 Gamma 1 -1 Subscript a 2 Subscript b 1 Gamma 1 -1 Subscript a 2 Subscript b 2 Gamma 1 -1 Subscript a 2 Subscript b 3 z Subscript a 2 -1 HypergeometricPFQRegularized 1 -1 Subscript a 2 Subscript b 1 1 -1 Subscript a 2 Subscript b 2 1 -1 Subscript a 2 Subscript b 3 Subscript a 1 -1 Subscript a 2 1 1 -1 Subscript a 2 Subscript a 3 1 z -1 UnitStep z -1 Subscript a 3 -1 Subscript b 1 -1 Gamma 1 -1 Subscript a 1 Subscript b 1 Gamma 1 -1 Subscript a 2 Subscript b 1 Gamma 1 -1 Subscript a 3 Subscript b 1 z Subscript b 1 HypergeometricPFQRegularized 1 -1 Subscript a 1 Subscript b 1 1 -1 Subscript a 2 Subscript b 1 1 -1 Subscript a 3 Subscript b 1 Subscript b 1 -1 Subscript b 2 1 Subscript b 1 -1 Subscript b 3 1 z UnitStep 1 -1 z Subscript a 2 -1 Subscript a 1 [/itex]

 Rule Form

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

 2001-10-29