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; }

 HypergeometricPFQ

 http://functions.wolfram.com/07.31.06.0034.01

 Input Form

 HypergeometricPFQ[{}, {Subscript[b, 1], Subscript[b, 2]}, z] \[Proportional] ((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]])/(2 Sqrt[3] Pi)) E^(3 z^(1/3)) z^((1/3) (1 - Subscript[b, 1] - Subscript[b, 2])) (1 + (-2 - 3 Subscript[b, 1]^2 + 3 Subscript[b, 2] - 3 Subscript[b, 2]^2 + 3 Subscript[b, 1] (1 + Subscript[b, 2]))/(9 z^(1/3)) + (1/(162 z^(2/3))) (4 + 9 Subscript[b, 1]^4 - 12 Subscript[b, 2] + 3 Subscript[b, 2]^2 - 12 Subscript[b, 2]^3 + 9 Subscript[b, 2]^4 - 6 Subscript[b, 1]^3 (2 + 3 Subscript[b, 2]) + 3 Subscript[b, 1]^2 (1 - 3 Subscript[b, 2] + 9 Subscript[b, 2]^2) - 3 Subscript[b, 1] (4 - 17 Subscript[b, 2] + 3 Subscript[b, 2]^2 + 6 Subscript[b, 2]^3)) + \[Ellipsis]) /; (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b", "1"], ",", SubscriptBox["b", "2"]]], "}"]], ",", "z"]], "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["b", "1"], "]"]], " ", RowBox[List["Gamma", "[", SubscriptBox["b", "2"], "]"]]]], RowBox[List["2", " ", SqrtBox["3"], " ", "\[Pi]"]]], SuperscriptBox["\[ExponentialE]", RowBox[List["3", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["1", "-", SubscriptBox["b", "1"], "-", SubscriptBox["b", "2"]]], ")"]]]]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["3", " ", SubsuperscriptBox["b", "1", "2"]]], "+", RowBox[List["3", " ", SubscriptBox["b", "2"]]], "-", RowBox[List["3", " ", SubsuperscriptBox["b", "2", "2"]]], "+", RowBox[List["3", " ", SubscriptBox["b", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["b", "2"]]], ")"]]]]]], RowBox[List["9", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]], "+", RowBox[List[FractionBox["1", RowBox[List["162", " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]]], RowBox[List["(", RowBox[List["4", "+", RowBox[List["9", " ", SubsuperscriptBox["b", "1", "4"]]], "-", RowBox[List["12", " ", SubscriptBox["b", "2"]]], "+", RowBox[List["3", " ", SubsuperscriptBox["b", "2", "2"]]], "-", RowBox[List["12", " ", SubsuperscriptBox["b", "2", "3"]]], "+", RowBox[List["9", " ", SubsuperscriptBox["b", "2", "4"]]], "-", RowBox[List["6", " ", SubsuperscriptBox["b", "1", "3"], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["3", " ", SubscriptBox["b", "2"]]]]], ")"]]]], "+", RowBox[List["3", " ", SubsuperscriptBox["b", "1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", SubscriptBox["b", "2"]]], "+", RowBox[List["9", " ", SubsuperscriptBox["b", "2", "2"]]]]], ")"]]]], "-", RowBox[List["3", " ", SubscriptBox["b", "1"], " ", RowBox[List["(", RowBox[List["4", "-", RowBox[List["17", " ", SubscriptBox["b", "2"]]], "+", RowBox[List["3", " ", SubsuperscriptBox["b", "2", "2"]]], "+", RowBox[List["6", " ", SubsuperscriptBox["b", "2", "3"]]]]], ")"]]]]]], ")"]]]], "+", "\[Ellipsis]"]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]

 MathML Form

 0 F 2 ( ; b 1 , b 2 ; z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["0", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox["\[Null]", InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox["z", HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] Γ ( b 1 ) Γ ( b 2 ) 2 3 π 3 z 3 z 1 3 ( 1 - b 1 - b 2 ) ( 1 + - 3 b 1 2 + 3 ( b 2 + 1 ) b 1 - 3 b 2 2 + 3 b 2 - 2 9 z 3 + 1 162 z 2 / 3 ( 9 b 1 4 - 6 ( 3 b 2 + 2 ) b 1 3 + 3 ( 9 b 2 2 - 3 b 2 + 1 ) b 1 2 - 3 ( 6 b 2 3 + 3 b 2 2 - 17 b 2 + 4 ) b 1 + 9 b 2 4 - 12 b 2 3 + 3 b 2 2 - 12 b 2 + 4 ) + ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional HypergeometricPFQ Subscript b 1 Subscript b 2 z Gamma Subscript b 1 Gamma Subscript b 2 2 3 1 2 -1 3 z 1 3 z 1 3 1 -1 Subscript b 1 -1 Subscript b 2 1 -3 Subscript b 1 2 3 Subscript b 2 1 Subscript b 1 -1 3 Subscript b 2 2 3 Subscript b 2 -2 9 z 1 3 -1 1 162 z 2 3 -1 9 Subscript b 1 4 -1 6 3 Subscript b 2 2 Subscript b 1 3 3 9 Subscript b 2 2 -1 3 Subscript b 2 1 Subscript b 1 2 -1 3 6 Subscript b 2 3 3 Subscript b 2 2 -1 17 Subscript b 2 4 Subscript b 1 9 Subscript b 2 4 -1 12 Subscript b 2 3 3 Subscript b 2 2 -1 12 Subscript b 2 4 Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", SubscriptBox["bb", "1"], "]"]], " ", RowBox[List["Gamma", "[", SubscriptBox["bb", "2"], "]"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["3", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List["1", "-", SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "2"]]], ")"]]]]], " ", RowBox[List["(", RowBox[List["1", "+", FractionBox[RowBox[List[RowBox[List["-", "2"]], "-", RowBox[List["3", " ", SubsuperscriptBox["bb", "1", "2"]]], "+", RowBox[List["3", " ", SubscriptBox["bb", "2"]]], "-", RowBox[List["3", " ", SubsuperscriptBox["bb", "2", "2"]]], "+", RowBox[List["3", " ", SubscriptBox["bb", "1"], " ", RowBox[List["(", RowBox[List["1", "+", SubscriptBox["bb", "2"]]], ")"]]]]]], RowBox[List["9", " ", SuperscriptBox["z", RowBox[List["1", "/", "3"]]]]]], "+", FractionBox[RowBox[List["4", "+", RowBox[List["9", " ", SubsuperscriptBox["bb", "1", "4"]]], "-", RowBox[List["12", " ", SubscriptBox["bb", "2"]]], "+", RowBox[List["3", " ", SubsuperscriptBox["bb", "2", "2"]]], "-", RowBox[List["12", " ", SubsuperscriptBox["bb", "2", "3"]]], "+", RowBox[List["9", " ", SubsuperscriptBox["bb", "2", "4"]]], "-", RowBox[List["6", " ", SubsuperscriptBox["bb", "1", "3"], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["3", " ", SubscriptBox["bb", "2"]]]]], ")"]]]], "+", RowBox[List["3", " ", SubsuperscriptBox["bb", "1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["3", " ", SubscriptBox["bb", "2"]]], "+", RowBox[List["9", " ", SubsuperscriptBox["bb", "2", "2"]]]]], ")"]]]], "-", RowBox[List["3", " ", SubscriptBox["bb", "1"], " ", RowBox[List["(", RowBox[List["4", "-", RowBox[List["17", " ", SubscriptBox["bb", "2"]]], "+", RowBox[List["3", " ", SubsuperscriptBox["bb", "2", "2"]]], "+", RowBox[List["6", " ", SubsuperscriptBox["bb", "2", "3"]]]]], ")"]]]]]], RowBox[List["162", " ", SuperscriptBox["z", RowBox[List["2", "/", "3"]]]]]], "+", "\[Ellipsis]"]], ")"]]]], RowBox[List["2", " ", SqrtBox["3"], " ", "\[Pi]"]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

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

 2001-10-29