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 KelvinBer

 http://functions.wolfram.com/03.18.06.0045.01

 Input Form

 KelvinBer[\[Nu], z] \[Proportional] (1/(2 Sqrt[2 Pi] Sqrt[-z])) (E^(z/Sqrt[2]) (E^((5 I Pi \[Nu])/2 + (3 Pi I)/8) E^((I z)/Sqrt[2]) (1 + O[1/z^2]) - (E^((3 I Pi \[Nu])/2 + (3 Pi I)/8) (1 + O[1/z^2]))/ E^((I z)/Sqrt[2])) + (E^((I Pi \[Nu])/2 + (Pi I)/8) E^((I z)/Sqrt[2]) (1 + O[1/z^2]) + (E^((3 I Pi \[Nu])/2 - (Pi I)/8) (1 + O[1/z^2]))/ E^((I z)/Sqrt[2]))/E^(z/Sqrt[2])) /; Inequality[Pi/2, Less, Arg[z], LessEqual, Pi] && (Abs[z] -> Infinity)

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", "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["5", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"], "+", FractionBox[RowBox[List["3", "\[Pi]", " ", "\[ImaginaryI]"]], "8"]]]], SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", "2"]], "]"]]]], ")"]]]], "-", " ", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["3", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"], "+", FractionBox[RowBox[List["3", "\[Pi]", " ", "\[ImaginaryI]"]], "8"]]]], SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", "2"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], RowBox[List["(", " ", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"], "+", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "8"]]]], SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["3", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"], "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "8"]]]], SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]]], RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", "2"]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], "/;", 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 ν ( z ) 1 2 2 π - z ( z 2 ( 5 π ν 2 + 3 π 8 z 2 ( 1 + O ( 1 z 2 ) ) TagBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "(", FractionBox["1", SuperscriptBox["z", "2"]], ")"]]]], ")"]], HypergeometricPFQ] - 3 π ν 2 + 3 π 8 - z 2 ( 1 + O ( 1 z 2 ) ) TagBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "(", FractionBox["1", SuperscriptBox["z", "2"]], ")"]]]], ")"]], HypergeometricPFQ] ) + - z 2 ( z 2 π ν 2 + π 8 ( 1 + O ( 1 z 2 ) ) TagBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["O", "(", FractionBox["1", SuperscriptBox["z", "2"]], ")"]]]], ")"]], HypergeometricPFQ] + - z 2 3 π ν 2 - π 8 ( 1 + O ( 1 z 2 ) ) ) ) /; π 2 < arg ( z ) π ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) Condition Proportional KelvinBer ν z 1 2 2 1 2 -1 z 1 2 -1 z 2 1 2 -1 5 ν 2 -1 3 8 -1 z 2 1 2 -1 HypergeometricPFQ 1 O 1 z 2 -1 -1 3 ν 2 -1 3 8 -1 -1 z 2 1 2 -1 HypergeometricPFQ 1 O 1 z 2 -1 -1 z 2 1 2 -1 z 2 1 2 -1 ν 2 -1 8 -1 HypergeometricPFQ 1 O 1 z 2 -1 -1 z 2 1 2 -1 3 ν 2 -1 -1 8 -1 1 O 1 z 2 -1 Inequality 2 -1 z Rule z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]_", ",", "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["5", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"], "+", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "8"]]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", "2"]], "]"]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"], "+", FractionBox[RowBox[List["3", " ", "\[Pi]", " ", "\[ImaginaryI]"]], "8"]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", "2"]], "]"]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", SqrtBox["2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"], "+", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "8"]]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", "2"]], "]"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[RowBox[List["3", " ", "\[ImaginaryI]", " ", "\[Pi]", " ", "\[Nu]"]], "2"], "-", FractionBox[RowBox[List["\[Pi]", " ", "\[ImaginaryI]"]], "8"]]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], SqrtBox["2"]]]]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", "2"]], "]"]]]], ")"]]]]]], ")"]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["2", " ", "\[Pi]"]]], " ", SqrtBox[RowBox[List["-", "z"]]]]]], "/;", RowBox[List[RowBox[List[FractionBox["\[Pi]", "2"], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", "\[Pi]"]], "&&", RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]]]]]]]]]]

 Date Added to functions.wolfram.com (modification date)

 2007-05-02