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variants of this functions
KelvinKei




Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[nu,z] > Series representations > Asymptotic series expansions > Expansions for any z in exponential form > Using exponential function with branch cut-free arguments > General case





http://functions.wolfram.com/03.19.06.0042.01









  


  








Input Form





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








Standard Form





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MathML Form







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





2007-05-02