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 KelvinBei

 http://functions.wolfram.com/03.13.06.0018.01

 Input Form

 KelvinBei[z] \[Proportional] (-(1/(2 Sqrt[2 Pi] Sqrt[z]))) (E^(z/Sqrt[2]) (E^(-((3 I Pi)/8) - (I z)/Sqrt[2]) + E^((3 I Pi)/8 + (I z)/Sqrt[2])) + (-E^(-((I Pi)/8) - (I z)/Sqrt[2]) + E^((I Pi)/8 + (I z)/Sqrt[2]))/ E^(z/Sqrt[2]) + (1/(8 z)) (E^(z/Sqrt[2]) (E^(-((I Pi)/8) - (I z)/Sqrt[2]) + E^((I Pi)/8 + (I z)/Sqrt[2])) + (E^(-((3 I Pi)/8) - (I z)/Sqrt[2]) - E^((3 I Pi)/8 + (I z)/Sqrt[2]))/E^(z/Sqrt[2])) + ((9 I)/(128 z^2)) (E^(z/Sqrt[2]) (E^(-((3 I Pi)/8) - (I z)/Sqrt[2]) - E^((3 I Pi)/8 + (I z)/Sqrt[2])) + (E^(-((I Pi)/8) - (I z)/Sqrt[2]) + E^((I Pi)/8 + (I z)/Sqrt[2]))/E^(z/Sqrt[2])) + ((75 I)/(1024 z^3)) (E^(z/Sqrt[2]) (E^(-((I Pi)/8) - (I z)/Sqrt[2]) - E^((I Pi)/8 + (I z)/Sqrt[2])) + (-E^(-((3 I Pi)/8) - (I z)/Sqrt[2]) - E^((3 I Pi)/8 + (I z)/Sqrt[2]))/E^(z/Sqrt[2])) + \[Ellipsis]) /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi] && (Abs[z] -> Infinity)

 Standard Form

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FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]]], "-", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]"]], "8"], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "8"]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]]], "+", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]"]], "8"], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[FractionBox[RowBox[List["75", " ", "\[ImaginaryI]", " "]], RowBox[List["1024", " ", SuperscriptBox["z", "3"]]]], RowBox[List["(", 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"\[ImaginaryI]", " ", "\[Pi]"]], "8"], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]]]]], ")"]]]]]], ")"]]]], "+", "\[Ellipsis]"]], ")"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]], "\[And]", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]

 MathML Form

 bei ( z ) - 1 2 2 π z ( - z 2 ( - - 1 8 ( π ) - z 2 + π 8 + z 2 ) + z 2 ( - 1 8 ( 3 π ) - z 2 + 3 π 8 + z 2 ) + 1 8 z ( z 2 ( - 1 8 ( π ) - z 2 + π 8 + z 2 ) + - z 2 ( - 1 8 ( 3 π ) - z 2 - 3 π 8 + z 2 ) ) + 9 128 z 2 ( - z 2 ( - 1 8 ( π ) - z 2 + π 8 + z 2 ) + z 2 ( - 1 8 ( 3 π ) - z 2 - 3 π 8 + z 2 ) ) + 75 1024 z 3 ( z 2 ( - 1 8 ( π ) - z 2 - π 8 + z 2 ) + - z 2 ( - - 1 8 ( 3 π ) - z 2 - 3 π 8 + z 2 ) ) + ) /; - π 2 < arg ( z ) π ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional KelvinBei z -1 1 2 2 1 2 z 1 2 -1 -1 z 2 1 2 -1 -1 -1 1 8 -1 z 2 1 2 -1 8 -1 z 2 1 2 -1 z 2 1 2 -1 -1 1 8 3 -1 z 2 1 2 -1 3 8 -1 z 2 1 2 -1 1 8 z -1 z 2 1 2 -1 -1 1 8 -1 z 2 1 2 -1 8 -1 z 2 1 2 -1 -1 z 2 1 2 -1 -1 1 8 3 -1 z 2 1 2 -1 -1 3 8 -1 z 2 1 2 -1 9 128 z 2 -1 -1 z 2 1 2 -1 -1 1 8 -1 z 2 1 2 -1 8 -1 z 2 1 2 -1 z 2 1 2 -1 -1 1 8 3 -1 z 2 1 2 -1 -1 3 8 -1 z 2 1 2 -1 75 1024 z 3 -1 z 2 1 2 -1 -1 1 8 -1 z 2 1 2 -1 -1 8 -1 z 2 1 2 -1 -1 z 2 1 2 -1 -1 -1 1 8 3 -1 z 2 1 2 -1 -1 3 8 -1 z 2 1 2 -1 Inequality -1 2 -1 z Rule z [/itex]

 Rule Form

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

 2007-05-02