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 KelvinBei

 http://functions.wolfram.com/03.17.06.0054.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2007-05-02