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; }

 KelvinKei

 http://functions.wolfram.com/03.19.06.0011.01

 Input Form

 KelvinKei[\[Nu], z] == ((I Pi^(3/2))/4) Sum[(2^k/(x^k k!)) ((2^(2 \[Nu]) Csc[Pi \[Nu]] Gamma[1 - \[Nu]] (E^((3 I Pi \[Nu])/4) HypergeometricPFQRegularized[ {(1 - \[Nu])/2, 1 - \[Nu]/2}, {(1 - k - \[Nu])/2, (2 - k - \[Nu])/2, 1 - \[Nu]}, -((I x^2)/4)] - HypergeometricPFQRegularized[{(1 - \[Nu])/2, 1 - \[Nu]/2}, {(1 - k - \[Nu])/2, (2 - k - \[Nu])/2, 1 - \[Nu]}, (I x^2)/4]/ E^((3 I Pi \[Nu])/4)))/(x^\[Nu] E^(2 I Pi \[Nu] Floor[Arg[z - x]/(2 Pi)])) + (x^\[Nu] (I + Cot[Pi \[Nu]]) Gamma[1 + \[Nu]] E^(2 I Pi \[Nu] Floor[Arg[z - x]/(2 Pi)]) ((-E^(-((3 I Pi \[Nu])/4))) HypergeometricPFQRegularized[ {(1 + \[Nu])/2, (2 + \[Nu])/2}, {(1 - k + \[Nu])/2, (2 - k + \[Nu])/2, 1 + \[Nu]}, -((I x^2)/4)] + HypergeometricPFQRegularized[{(1 + \[Nu])/2, (2 + \[Nu])/2}, {(1 - k + \[Nu])/2, (2 - k + \[Nu])/2, 1 + \[Nu]}, (I x^2)/4]/ E^((5 I Pi \[Nu])/4)))/2^(2 \[Nu])) (z - x)^k, {k, 0, Infinity}] /; !Element[\[Nu], Integers] && Element[x, Reals] && x < 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", "\n", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]], "4"], "\t", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", "k"], SuperscriptBox["x", RowBox[List["-", "k"]]]]], RowBox[List["k", "!"]]], RowBox[List["(", " ", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["2", " ", "\[Nu]"]]], " ", SuperscriptBox["x", RowBox[List["-", "\[Nu]"]]], RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Nu]"]], "]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", "x"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "4"]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "k", "-", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "-", "k", "-", "\[Nu]"]], "2"], ",", RowBox[List["1", "-", "\[Nu]"]]]], "}"]], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["x", "2"]]], "4"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "4"]]]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "k", "-", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "-", "k", "-", "\[Nu]"]], "2"], ",", RowBox[List["1", "-", "\[Nu]"]]]], "}"]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["x", "2"]]], "4"]]], "]"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "2"]], " ", "\[Nu]"]]], SuperscriptBox["x", "\[Nu]"], RowBox[List["(", RowBox[List["\[ImaginaryI]", "+", RowBox[List["Cot", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], ")"]], RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", "x"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "4"]]]]]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "k", "+", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "-", "k", "+", "\[Nu]"]], "2"], ",", RowBox[List["1", "+", "\[Nu]"]]]], "}"]], ",", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["x", "2"]]], "4"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["5", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "4"]]]], RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "k", "+", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "-", "k", "+", "\[Nu]"]], "2"], ",", RowBox[List["1", "+", "\[Nu]"]]]], "}"]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["x", "2"]]], "4"]]], "]"]]]]]], ")"]]]]]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "x"]], ")"]], "k"]]]]]]]]], "/;", RowBox[List[RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["\[Nu]", ",", "Integers"]], "]"]], "]"]], "\[And]", RowBox[List["x", "\[Element]", "Reals"]], "\[And]", RowBox[List["x", "<", "0"]]]]]]]]

 MathML Form

 kei ν ( z ) π 3 / 2 4 k = 0 2 k x - k k ! ( 2 2 ν - 2 π ν arg ( z - x ) 2 π csc ( π ν ) Γ ( 1 - ν ) ( 3 π ν 4 2 F ~ 3 ( 1 - ν 2 , 1 - ν 2 ; 1 2 ( - k - ν + 1 ) , 1 2 ( - k - ν + 2 ) , 1 - ν ; - x 2 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox[OverscriptBox["F", "~"], "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "-", "\[Nu]", "+", "1"]], ")"]]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "-", "\[Nu]", "+", "2"]], ")"]]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", "\[Nu]"]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["x", "2"]]], "4"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQRegularized] - - 3 π ν 4 2 F ~ 3 ( 1 - ν 2 , 1 - ν 2 ; 1 2 ( - k - ν + 1 ) , 1 2 ( - k - ν + 2 ) , 1 - ν ; x 2 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox[OverscriptBox["F", "~"], "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "-", "\[Nu]", "+", "1"]], ")"]]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "-", "\[Nu]", "+", "2"]], ")"]]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", "\[Nu]"]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["x", "2"]]], "4"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQRegularized] ) x - ν + 2 - 2 ν 2 π ν arg ( z - x ) 2 π ( + cot ( π ν ) ) Γ ( ν + 1 ) ( - 5 π ν 4 2 F ~ 3 ( ν + 1 2 , ν + 2 2 ; 1 2 ( - k + ν + 1 ) , 1 2 ( - k + ν + 2 ) , ν + 1 ; x 2 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox[OverscriptBox["F", "~"], "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox[RowBox[List["\[Nu]", "+", "2"]], "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "+", "\[Nu]", "+", "1"]], ")"]]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "+", "\[Nu]", "+", "2"]], ")"]]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["\[Nu]", "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["x", "2"]]], "4"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQRegularized] - - 3 π ν 4 2 F ~ 3 ( ν + 1 2 , ν + 2 2 ; 1 2 ( - k + ν + 1 ) , 1 2 ( - k + ν + 2 ) , ν + 1 ; - x 2 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox[OverscriptBox["F", "~"], "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox[RowBox[List["\[Nu]", "+", "2"]], "2"], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "+", "\[Nu]", "+", "1"]], ")"]]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "+", "\[Nu]", "+", "2"]], ")"]]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["\[Nu]", "+", "1"]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQRegularized, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["x", "2"]]], "4"]]], HypergeometricPFQRegularized, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQRegularized[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQRegularized] ) x ν ) ( z - x ) k /; ν TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] x TagBox["\[DoubleStruckCapitalR]", Function[List[], Reals]] x < 0 Condition KelvinKei ν z 3 2 4 -1 k 0 2 k x -1 k k -1 2 2 ν -2 ν z -1 x 2 -1 ν Gamma 1 -1 ν 3 ν 4 -1 HypergeometricPFQRegularized 1 -1 ν 2 -1 1 -1 ν 2 -1 1 2 -1 k -1 ν 1 1 2 -1 k -1 ν 2 1 -1 ν -1 x 2 4 -1 -1 -1 3 ν 4 -1 HypergeometricPFQRegularized 1 -1 ν 2 -1 1 -1 ν 2 -1 1 2 -1 k -1 ν 1 1 2 -1 k -1 ν 2 1 -1 ν x 2 4 -1 x -1 ν 2 -2 ν 2 ν z -1 x 2 -1 ν Gamma ν 1 -1 5 ν 4 -1 HypergeometricPFQRegularized ν 1 2 -1 ν 2 2 -1 1 2 -1 k ν 1 1 2 -1 k ν 2 ν 1 x 2 4 -1 -1 -1 3 ν 4 -1 HypergeometricPFQRegularized ν 1 2 -1 ν 2 2 -1 1 2 -1 k ν 1 1 2 -1 k ν 2 ν 1 -1 x 2 4 -1 x ν z -1 x k ν x x 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", "k"], " ", SuperscriptBox["x", RowBox[List["-", "k"]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["2", RowBox[List["2", " ", "\[Nu]"]]], " ", SuperscriptBox["x", RowBox[List["-", "\[Nu]"]]], " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "\[Nu]"]], "]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]", " ", RowBox[List["Floor", 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"+", RowBox[List["Cot", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]], ")"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["Arg", "[", RowBox[List["z", "-", "x"]], "]"]], RowBox[List["2", " ", "\[Pi]"]]], "]"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", RowBox[List["(", RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], ")"]]]]]]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List["1", "-", "k", "+", 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"\[Nu]"]], ")"]]]], ",", RowBox[List["1", "+", "\[Nu]"]]]], "}"]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["x", "2"]]], "4"]]], "]"]]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", "x"]], ")"]], "k"]]], RowBox[List["k", "!"]]]]]]], "/;", RowBox[List[RowBox[List["!", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]], "&&", RowBox[List["x", "\[Element]", "Reals"]], "&&", RowBox[List["x", "<", "0"]]]]]]]]]]

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

 2007-05-02

© 1998-2013 Wolfram Research, Inc.