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; }

 KelvinBei

 http://functions.wolfram.com/03.13.06.0039.01

 Input Form

 KelvinBei[z] \[Proportional] Piecewise[{{((-1)^(1/8) (-(-1)^(3/4) - (-1)^(1/4) E^(2 (-1)^(1/4) z) - E^(I Sqrt[2] z) + I E^(Sqrt[2] z)))/(E^((-1)^(1/4) z) (2 Sqrt[2 Pi] Sqrt[z])), Inequality[-(1/4), Less, Arg[z]/Pi, LessEqual, 1/4]}, {((-1)^(1/8) (-(-1)^(3/4) + (-1)^(1/4) E^(2 (-1)^(1/4) z) - E^(I Sqrt[2] z) + I E^(Sqrt[2] z)))/(E^((-1)^(1/4) z) (2 Sqrt[2 Pi] Sqrt[z])), Inequality[1/4, Less, Arg[z]/Pi, LessEqual, 3/4]}, {((-1)^(1/8) (-(-1)^(3/4) + (-1)^(1/4) E^(2 (-1)^(1/4) z) - E^(I Sqrt[2] z) - I E^(Sqrt[2] z)))/(E^((-1)^(1/4) z) (2 Sqrt[2 Pi] Sqrt[z])), Arg[z]/Pi > 3/4}, {((-1)^(1/8) (-(-1)^(3/4) - (-1)^(1/4) E^(2 (-1)^(1/4) z) + E^(I Sqrt[2] z) + I E^(Sqrt[2] z)))/(E^((-1)^(1/4) z) (2 Sqrt[2 Pi] Sqrt[z])), Inequality[-(3/4), Less, Arg[z]/Pi, LessEqual, -(1/4)]}}, ((-1)^(1/8) ((-1)^(3/4) - (-1)^(1/4) E^(2 (-1)^(1/4) z) + E^(I Sqrt[2] z) + I E^(Sqrt[2] z)))/(E^((-1)^(1/4) z) (2 Sqrt[2 Pi] Sqrt[z]))] /; (Abs[z] -> Infinity)

 Standard Form

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

 MathML Form

 bei ( z ) - 1 8 - - 1 4 z ( - ( - 1 ) 3 / 4 - - 1 4 2 - 1 4 z - 2 z + 2 z ) 2 2 π z - 1 4 < arg ( z ) π 1 4 - 1 8 - - 1 4 z ( - ( - 1 ) 3 / 4 + - 1 4 2 - 1 4 z - 2 z + 2 z ) 2 2 π z 1 4 < arg ( z ) π 3 4 - 1 8 - - 1 4 z ( - ( - 1 ) 3 / 4 + - 1 4 2 - 1 4 z - 2 z - 2 z ) 2 2 π z arg ( z ) π > 3 4 - 1 8 - - 1 4 z ( - ( - 1 ) 3 / 4 - - 1 4 2 - 1 4 z + 2 z + 2 z ) 2 2 π z - 3 4 < arg ( z ) π - 1 4 - 1 8 - - 1 4 z ( ( - 1 ) 3 / 4 - - 1 4 2 - 1 4 z + 2 z + 2 z ) 2 2 π z True TagBox["True", "PiecewiseDefault", Rule[AutoDelete, False], Rule[DeletionWarning, True]] /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional KelvinBei z -1 1 8 -1 -1 1 4 z -1 -1 3 4 -1 -1 1 4 2 -1 1 4 z -1 2 1 2 z 2 1 2 z 2 2 1 2 z 1 2 -1 Inequality -1 1 4 z -1 1 4 -1 1 8 -1 -1 1 4 z -1 -1 3 4 -1 1 4 2 -1 1 4 z -1 2 1 2 z 2 1 2 z 2 2 1 2 z 1 2 -1 Inequality 1 4 z -1 3 4 -1 1 8 -1 -1 1 4 z -1 -1 3 4 -1 1 4 2 -1 1 4 z -1 2 1 2 z -1 2 1 2 z 2 2 1 2 z 1 2 -1 z -1 3 4 -1 1 8 -1 -1 1 4 z -1 -1 3 4 -1 -1 1 4 2 -1 1 4 z 2 1 2 z 2 1 2 z 2 2 1 2 z 1 2 -1 Inequality -1 3 4 z -1 -1 1 4 -1 1 8 -1 -1 1 4 z -1 3 4 -1 -1 1 4 2 -1 1 4 z 2 1 2 z 2 1 2 z 2 2 1 2 z 1 2 -1 Rule z [/itex]

 Rule Form

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

 2007-05-02