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/07.34.03.0727.01

 Input Form

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

 Standard Form

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

 MathML Form

 G 1 , 3 2 , 1 ( z a 1 b 1 , b 2 , b 3 ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["1", ",", "3"]], RowBox[List["2", ",", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[TagBox[SubscriptBox["a", "1"], 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]] π csc ( π ( b 2 - b 1 ) ) ( Γ ( 1 - a 1 + b 1 ) z b 1 1 F ~ 2 ( 1 - a 1 + b 1 ; b 1 - b 2 + 1 , b 1 - b 3 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[TagBox[RowBox[List["1", "-", SubscriptBox["a", "1"], "+", 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] - Γ ( 1 - a 1 + b 2 ) z b 2 1 F ~ 2 ( 1 - a 1 + b 2 ; 1 - b 1 + b 2 , b 2 - b 3 + 1 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["1", TraditionalForm]], SubscriptBox[OverscriptBox["F", "~"], FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[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["b", "1"], "+", SubscriptBox["b", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True]], ",", TagBox[RowBox[List[SubscriptBox["b", "2"], "-", 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] ) /; b 2 - b 1 TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] Condition MeijerG Subscript a 1 Subscript b 1 Subscript b 2 Subscript b 3 z Subscript b 2 -1 Subscript b 1 Gamma 1 -1 Subscript a 1 Subscript b 1 z Subscript b 1 HypergeometricPFQRegularized 1 -1 Subscript a 1 Subscript b 1 Subscript b 1 -1 Subscript b 2 1 Subscript b 1 -1 Subscript b 3 1 z -1 Gamma 1 -1 Subscript a 1 Subscript b 2 z Subscript b 2 HypergeometricPFQRegularized 1 -1 Subscript a 1 Subscript b 2 1 -1 Subscript b 1 Subscript b 2 Subscript b 2 -1 Subscript b 3 1 z Subscript b 2 -1 Subscript b 1 [/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["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"]]], "}"]], ",", RowBox[List["{", SubscriptBox["b_", "3"], "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["bb", "1"]]], "+", SubscriptBox["bb", "2"]]], ")"]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["bb", "1"]]], "]"]], " ", SuperscriptBox["z", SubscriptBox["bb", "1"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["bb", "1"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "3"]]]]], "}"]], ",", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["bb", "2"]]], "]"]], " ", SuperscriptBox["z", SubscriptBox["bb", "2"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["bb", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["bb", "1"], "+", SubscriptBox["bb", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["bb", "2"], "-", SubscriptBox["bb", "3"]]]]], "}"]], ",", "z"]], "]"]]]]]], ")"]]]], "/;", RowBox[List["!", RowBox[List[RowBox[List[SubscriptBox["bb", "2"], "-", SubscriptBox["bb", "1"]]], "\[Element]", "Integers"]]]]]]]]]]

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

 2001-10-29