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/07.34.03.0321.01

 Input Form

 MeijerG[{{Subscript[a, 1]}, {Subscript[a, 2]}}, {{Subscript[b, 1]}, {Subscript[b, 2]}}, z] == Gamma[1 - Subscript[a, 1] + Subscript[b, 1]] ((1/Gamma[Subscript[a, 2] - Subscript[b, 1]]) z^Subscript[b, 1] HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 1], 1 - Subscript[a, 2] + Subscript[b, 1]}, {1 + Subscript[b, 1] - Subscript[b, 2]}, z] UnitStep[1 - Abs[z]] + (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/z] UnitStep[Abs[z] - 1])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", SubscriptBox["a", "1"], "}"]], ",", RowBox[List["{", SubscriptBox["a", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", SubscriptBox["b", "1"], "}"]], ",", RowBox[List["{", SubscriptBox["b", "2"], "}"]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["b", "1"]]], "]"]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["a", "2"], "-", SubscriptBox["b", "1"]]], "]"]]], SuperscriptBox["z", SubscriptBox["b", "1"]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["b", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["a", "2"], "+", SubscriptBox["b", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]], "}"]], ",", "z"]], "]"]], RowBox[List["UnitStep", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z", "]"]]]], "]"]]]], "+", RowBox[List[FractionBox["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["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["a", "2"]]], "}"]], ",", FractionBox["1", "z"]]], "]"]], RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "-", "1"]], "]"]]]]]], ")"]]]]]]]]

 MathML Form

 G 2 , 2 1 , 1 ( z a 1 , a 2 b 1 , b 2 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["2", ",", "2"]], RowBox[List["1", ",", "1"]]], "\[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]]]]], List[RowBox[List[TagBox[SubscriptBox["b", "1"], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] Γ ( 1 - a 1 + b 1 ) ( θ UnitStep ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" - 1 ) Γ ( a 1 - b 2 ) z a 1 - 1 2 F ~ 1 ( 1 - a 1 + b 1 , 1 - a 1 + b 2 ; 1 - a 1 + a 2 ; 1 z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", 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[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"], "+", SubscriptBox["a", "2"]]], 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 ( 1 - "\[LeftBracketingBar]" z "\[RightBracketingBar]" ) Γ ( a 2 - b 1 ) z b 1 2 F ~ 1 ( 1 - a 1 + b 1 , 1 - a 2 + b 1 ; b 1 - b 2 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["1", 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]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List[SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"], "+", "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] ) MeijerG Subscript a 1 Subscript a 2 Subscript b 1 Subscript b 2 z Gamma 1 -1 Subscript a 1 Subscript b 1 UnitStep z -1 Gamma Subscript a 1 -1 Subscript b 2 -1 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 a 2 1 z -1 UnitStep 1 -1 z Gamma Subscript a 2 -1 Subscript b 1 -1 z Subscript b 1 HypergeometricPFQRegularized 1 -1 Subscript a 1 Subscript b 1 1 -1 Subscript a 2 Subscript b 1 Subscript b 1 -1 Subscript b 2 1 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", SubscriptBox["a_", "1"], "}"]], ",", RowBox[List["{", SubscriptBox["a_", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", SubscriptBox["b_", "1"], "}"]], ",", RowBox[List["{", SubscriptBox["b_", "2"], "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["bb", "1"]]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", SubscriptBox["bb", "1"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["bb", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["aa", "2"], "+", SubscriptBox["bb", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "2"]]], "}"]], ",", "z"]], "]"]], " ", RowBox[List["UnitStep", "[", RowBox[List["1", "-", RowBox[List["Abs", "[", "z", "]"]]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["aa", "2"], "-", SubscriptBox["bb", "1"]]], "]"]]], "+", FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List[RowBox[List["-", "1"]], "+", SubscriptBox["aa", "1"]]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["bb", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["bb", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["aa", "2"]]], "}"]], ",", FractionBox["1", "z"]]], "]"]], " ", RowBox[List["UnitStep", "[", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "-", "1"]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["aa", "1"], "-", SubscriptBox["bb", "2"]]], "]"]]]]], ")"]]]]]]]]

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

 2001-10-29