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/03.20.06.0049.01

 Input Form

 KelvinKer[\[Nu], z] \[Proportional] Piecewise[{{(((-1)^(1/8) Sqrt[Pi])/(2 Sqrt[2 z])) ((-(-1)^(3/4)) E^((-(-1)^(1/4)) z - (I Pi \[Nu])/2) + E^((-1)^(3/4) z + (I Pi \[Nu])/2)), Arg[z] <= Pi/4}, {(((-1)^(1/8) Sqrt[Pi])/(2 Sqrt[2 z])) ((-(-1)^(3/4)) E^((-(-1)^(1/4)) z - (I Pi \[Nu])/2) + (-1)^(1/4) E^((-1)^(1/4) z + (I Pi \[Nu])/2) + E^((-1)^(3/4) z + (I Pi \[Nu])/2) + (-1)^(1/4) E^((-1)^(1/4) z - (3 I Pi \[Nu])/2)), Inequality[Pi/4, Less, Arg[z], LessEqual, (3 Pi)/4]}}, (((-1)^(1/8) Sqrt[Pi])/(2 Sqrt[2 z])) ((-(-1)^(3/4)) E^((-(-1)^(1/4)) z - (I Pi \[Nu])/2) + I E^((-(-1)^(3/4)) z - (I Pi \[Nu])/2) + (-1)^(1/4) E^((-1)^(1/4) z + (I Pi \[Nu])/2) + E^((-1)^(3/4) z + (I Pi \[Nu])/2) + (-1)^(1/4) E^((-1)^(1/4) z - (3 I Pi \[Nu])/2) + I E^((-(-1)^(3/4)) z + (3 I Pi \[Nu])/2))] /; (Abs[z] -> Infinity) && !Element[\[Nu], Integers]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Proportional]", RowBox[List["Piecewise", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", SqrtBox["\[Pi]"]]], RowBox[List["2", " ", SqrtBox[RowBox[List["2", "z"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], 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"[", "z", "]"]], "\[LessEqual]", FractionBox[RowBox[List["3", "\[Pi]"]], "4"]]]]], "}"]]]], "}"]], ",", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], SqrtBox["\[Pi]"]]], RowBox[List["2", " ", SqrtBox[RowBox[List["2", "z"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", "z"]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]], "+", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]], "-", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "+", RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", "z"]], "+", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]]]], ")"]]]]]], "]"]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "\[And]", RowBox[List["Not", "[", RowBox[List["Element", "[", RowBox[List["\[Nu]", ",", "Integers"]], "]"]], "]"]]]]]]]]

 MathML Form

 ker ν ( z ) - 1 8 π 2 2 z ( - ( - 1 ) 3 / 4 - - 1 4 z - π ν 2 + ( - 1 ) 3 / 4 z + π ν 2 ) arg ( z ) π 4 - 1 8 π 2 2 z ( - ( - 1 ) 3 / 4 - - 1 4 z - π ν 2 + - 1 4 - 1 4 z + π ν 2 + ( - 1 ) 3 / 4 z + π ν 2 + - 1 4 - 1 4 z - 3 π ν 2 ) π 4 < arg ( z ) 3 π 4 - 1 8 π 2 2 z ( - ( - 1 ) 3 / 4 - - 1 4 z - π ν 2 + - ( - 1 ) 3 / 4 z - π ν 2 + - 1 4 - 1 4 z + π ν 2 + ( - 1 ) 3 / 4 z + π ν 2 + - 1 4 - 1 4 z - 3 π ν 2 + 3 π ν 2 - ( - 1 ) 3 / 4 z ) True TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] Proportional KelvinKer ν z -1 1 8 1 2 2 2 z 1 2 -1 -1 -1 3 4 -1 -1 1 4 z -1 ν 2 -1 -1 3 4 z ν 2 -1 z 4 -1 -1 1 8 1 2 2 2 z 1 2 -1 -1 -1 3 4 -1 -1 1 4 z -1 ν 2 -1 -1 1 4 -1 1 4 z ν 2 -1 -1 3 4 z ν 2 -1 -1 1 4 -1 1 4 z -1 3 ν 2 -1 Inequality 4 -1 z 3 4 -1 -1 1 8 1 2 2 2 z 1 2 -1 -1 -1 3 4 -1 -1 1 4 z -1 ν 2 -1 -1 -1 3 4 z -1 ν 2 -1 -1 1 4 -1 1 4 z ν 2 -1 -1 3 4 z ν 2 -1 -1 1 4 -1 1 4 z -1 3 ν 2 -1 3 ν 2 -1 -1 -1 3 4 z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Piecewise]", GridBox[List[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "8"]]], " ", SqrtBox["\[Pi]"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"]]]]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]], "+", 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 Date Added to functions.wolfram.com (modification date)

 2007-05-02