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 KelvinBer

 http://functions.wolfram.com/03.14.06.0026.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinBer", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox["1", RowBox[List["2", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SqrtBox[RowBox[List["-", "z"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["z", SqrtBox["2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]"]], "8"], "-", 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["-", 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RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]"]], "8"]]], "-", 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["8", " ", "z"]]], "+", FractionBox[RowBox[List["9", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox["z", SqrtBox["2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]"]], "8"], "-", 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["-", 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["128", " ", SuperscriptBox["z", "2"]]]], "-", FractionBox[RowBox[List["75", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", 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[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]"]], "8"]]], "-", 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["1024", " ", SuperscriptBox["z", "3"]]]], "+", "\[Ellipsis]"]], ")"]]]]]], "/;", 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

 ber ( z ) 1 2 2 π - z ( - z 2 ( - 1 8 ( π ) - z 2 + π 8 + z 2 ) + z 2 ( - 3 π 8 - 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 ( - 3 π 8 - 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 KelvinBer z 1 2 2 1 2 -1 z 1 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 3 8 -1 -1 z 2 1 2 -1 3 8 -1 z 2 1 2 -1 -1 1 8 z -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 8 3 -1 z 2 1 2 -1 3 8 -1 z 2 1 2 -1 9 128 z 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 3 8 -1 -1 z 2 1 2 -1 -1 3 8 -1 z 2 1 2 -1 -1 75 1024 z 3 -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 1 8 3 -1 z 2 1 2 -1 3 8 -1 z 2 1 2 -1 Inequality 2 -1 z Rule z [/itex]

 Rule Form

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

 2007-05-02