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/07.34.03.0015.01

 Input Form

 MeijerG[{{a, Subscript[a, 2], \[Ellipsis], Subscript[a, p]}, {}}, {{0}, {a + 1, Subscript[b, 2], \[Ellipsis], Subscript[b, q]}}, z] == (-(Product[Gamma[1 - Subscript[a, j]], {j, 2, p}]/ Product[Gamma[1 - Subscript[b, j]], {j, 2, q}])) (a HypergeometricPFQ[{1 - Subscript[a, 2], \[Ellipsis], 1 - Subscript[a, p]}, {1 - Subscript[b, 2], \[Ellipsis], 1 - Subscript[b, q]}, -z] + ((z Product[1 - Subscript[a, j], {j, 2, p}])/Product[1 - Subscript[b, j], {j, 2, q}]) HypergeometricPFQ[{2 - Subscript[a, 2], \[Ellipsis], 2 - Subscript[a, p]}, {2 - Subscript[b, 2], \[Ellipsis], 2 - Subscript[b, q]}, -z])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["a", ",", SubscriptBox["a", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["a", "p"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["a", "+", "1"]], ",", SubscriptBox["b", "2"], ",", "\[Ellipsis]", ",", SubscriptBox["b", "q"]]], "}"]]]], "}"]], ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], "p"], RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["a", "j"]]], "]"]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], "q"], RowBox[List["Gamma", "[", RowBox[List["1", "-", SubscriptBox["b", "j"]]], "]"]]]]]]], RowBox[List["(", RowBox[List[RowBox[List["a", " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["a", "2"]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "-", SubscriptBox["a", "p"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["b", "2"]]], ",", "\[Ellipsis]", ",", RowBox[List["1", "-", SubscriptBox["b", "q"]]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]], "+", RowBox[List[FractionBox[RowBox[List["z", RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], "p"], RowBox[List["(", RowBox[List["1", "-", SubscriptBox["a", "j"]]], ")"]]]]]], RowBox[List[UnderoverscriptBox["\[Product]", RowBox[List["j", "=", "2"]], "q"], RowBox[List["(", RowBox[List["1", "-", SubscriptBox["b", "j"]]], ")"]]]]], RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["a", "2"]]], ",", "\[Ellipsis]", ",", RowBox[List["2", "-", SubscriptBox["a", "p"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["2", "-", SubscriptBox["b", "2"]]], ",", "\[Ellipsis]", ",", RowBox[List["2", "-", SubscriptBox["b", "q"]]]]], "}"]], ",", RowBox[List["-", "z"]]]], "]"]]]]]], ")"]]]]]]]]

 MathML Form

 G p , q + 1 1 , p ( z a , a 2 , , a p 0 , a + 1 , b 2 , , b q ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["p", ",", RowBox[List["q", "+", "1"]]]], RowBox[List["1", ",", "p"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["a", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "+", "1"]], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] - j = 2 p Γ ( 1 - a j ) j = 2 q Γ ( 1 - b j ) ( z j = 2 p ( 1 - a j ) j = 2 q ( 1 - b j ) p + 1 F q + 1 ( 2 - a 2 , , 2 - a p ; 2 - b 2 , , 2 - b q ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["p", "+", "1"]], TraditionalForm]], SubscriptBox["F", FormBox[RowBox[List["q", "+", "1"]], TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["2", "-", SubscriptBox["a", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["2", "-", SubscriptBox["a", "p"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["2", "-", SubscriptBox["b", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["2", "-", SubscriptBox["b", "q"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] + a 3 F 3 ( 1 - a 2 , , 1 - a p ; 1 - b 2 , , 1 - b q ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "p"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "q"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] ) G p , q + 1 1 , p ( z a , a 2 , , a p 0 , a + 1 , b 2 , , b q ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["p", ",", RowBox[List["q", "+", "1"]]]], RowBox[List["1", ",", "p"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["a", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "p"], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["0", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "+", "1"]], MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], MeijerG, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", MeijerG, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "q"], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, True]] - j = 2 p Γ ( 1 - a j ) j = 2 q Γ ( 1 - b j ) ( z j = 2 p ( 1 - a j ) j = 2 q ( 1 - b j ) p + 1 F q + 1 ( 2 - a 2 , , 2 - a p ; 2 - b 2 , , 2 - b q ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox[RowBox[List["p", "+", "1"]], TraditionalForm]], SubscriptBox["F", FormBox[RowBox[List["q", "+", "1"]], TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["2", "-", SubscriptBox["a", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["2", "-", SubscriptBox["a", "p"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["2", "-", SubscriptBox["b", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["2", "-", SubscriptBox["b", "q"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] + a 3 F 3 ( 1 - a 2 , , 1 - a p ; 1 - b 2 , , 1 - b q ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["3", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["a", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["a", "p"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", SubscriptBox["b", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox["\[Ellipsis]", HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", SubscriptBox["b", "q"]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, True]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, True]], HypergeometricPFQ] ) [/itex]

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

 2001-10-29