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; }

 KelvinKer

 http://functions.wolfram.com/03.16.06.0034.01

 Input Form

 KelvinKer[z] \[Proportional] (-(1/(E^(((1 + I) z)/Sqrt[2]) (8 Sqrt[2 Pi] Sqrt[(-(-1)^(1/4)) z] ((-1)^(3/4) z)^(3/2))))) (Sqrt[(-1)^(3/4) z] (-((Pi (I Sqrt[2] E^(I Sqrt[2] z) z + (1 + I) E^(Sqrt[2] z) ((-2 + 2 I) Sqrt[2] z + Sqrt[(-I) z^2])))/Sqrt[2]) + 4 (E^(I Sqrt[2] z) z - (-1)^(3/4) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z])) + Sqrt[(-(-1)^(1/4)) z] (Pi ((4 - 3 I E^((1 + I) Sqrt[2] z)) z + ((3 - 3 I) Sqrt[I z^2])/ Sqrt[2]) + 4 (E^((1 + I) Sqrt[2] z) z + (-1)^(1/4) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z]))) (1 + O[1/z^4]) /; (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", "z", "]"]], "\[Proportional]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], SqrtBox["2"]]]]], RowBox[List["8", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox["2"], " ", "z"]], "+", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]], ")"]]]]]], ")"]]]], SqrtBox["2"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]]]]]], " ", ")"]], "z"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", RowBox[List["3", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]], SqrtBox["2"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", "4"]], "]"]]]], ")"]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]

 MathML Form

 ker ( z ) - - ( 1 + ) z 2 8 2 π - - 1 4 z ( ( - 1 ) 3 / 4 z ) 3 / 2 ( ( - 1 ) 3 / 4 z ( 4 ( 2 z z - ( - 1 ) 3 / 4 2 z - z 2 ) ( log ( - - 1 4 z ) - log ( z ) ) - π ( 2 2 z z + 2 z ( 1 + ) ( 2 ( - 2 + 2 ) z + - z 2 ) ) 2 ) + - - 1 4 z ( π ( z 2 ( 3 - 3 ) 2 - 3 ( 1 + ) 2 z z + 4 z ) + 4 ( ( 1 + ) 2 z z + - 1 4 z 2 ) ( log ( ( - 1 ) 3 / 4 z ) - log ( z ) ) ) ) ( 1 + O ( 1 z 4 ) ) TagBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "(", FractionBox["1", SuperscriptBox["z", "4"]], ")"]]]], ")"]], HypergeometricPFQ] /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional KelvinKer z -1 -1 1 z 2 1 2 -1 8 2 1 2 -1 -1 1 4 z 1 2 -1 3 4 z 3 2 -1 -1 3 4 z 1 2 4 2 1 2 z z -1 -1 3 4 2 1 2 z -1 z 2 1 2 -1 -1 1 4 z -1 z -1 2 1 2 2 1 2 z z 2 1 2 z 1 2 1 2 -2 2 z -1 z 2 1 2 2 1 2 -1 -1 -1 1 4 z 1 2 z 2 1 2 3 -3 2 1 2 -1 -1 3 1 2 1 2 z z 4 z 4 1 2 1 2 z z -1 1 4 z 2 1 2 -1 3 4 z -1 z HypergeometricPFQ 1 O 1 z 4 -1 Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKer", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", "z"]], SqrtBox["2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["2", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox["2"], " ", "z"]], "+", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]], ")"]]]]]], ")"]]]], SqrtBox["2"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["\[ImaginaryI]", " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "-", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SqrtBox["2"], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["4", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]]]]]], ")"]], " ", "z"]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["3", "-", RowBox[List["3", " ", "\[ImaginaryI]"]]]], ")"]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]], SqrtBox["2"]]]], ")"]]]], "+", RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"], " ", "z"]]], " ", "z"]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Log", "[", "z", "]"]]]], "+", RowBox[List["Log", "[", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", "4"]], "]"]]]], ")"]]]], RowBox[List["8", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], "/;", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

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

 2007-05-02