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variants of this functions
KelvinKei




Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[z] > Series representations > Generalized power series > Expansions at z==0 > For small integer powers of the function





http://functions.wolfram.com/03.15.06.0016.01









  


  








Input Form





KelvinKei[z]^2 \[Proportional] (1/32) (Pi^2 + (-4 EulerGamma + Log[16])^2 + 16 (2 EulerGamma + Log[z/4]) Log[z] + (1/32) (16 EulerGamma^2 + Pi^2 - 8 EulerGamma (5 + Log[16]) + 8 (4 + 2 Log[2]^2 + Log[32]) + 8 Log[z] (-5 + 4 EulerGamma - 4 Log[2] + 2 Log[z])) z^4 + (1/221184) (536 + 9 Pi^2 + 12 EulerGamma (-43 + 12 EulerGamma - 24 Log[2]) + 516 Log[2] + Log[4096]^2 + 12 Log[z] (-43 + 24 EulerGamma - 24 Log[2] + 12 Log[z])) z^8 + \[Ellipsis]) - (1/32) ((4 EulerGamma - Pi - 4 Log[2] + 4 Log[z]) (4 EulerGamma + Pi - 4 Log[2] + 4 Log[z]) + (1/32) (3 Pi^2 - 8 (4 + 6 Log[2]^2 + Log[2048]) + 8 EulerGamma (11 - 6 EulerGamma + Log[4096]) + 8 (11 - 12 EulerGamma + Log[4096] - 6 Log[z]) Log[z]) z^4 + (1/221184) (1680 EulerGamma^2 - 105 Pi^2 - 4 EulerGamma (1217 + 840 Log[2]) + 4 (838 + Log[2] (1217 + 420 Log[2])) + 4 Log[z] (-1217 + 840 EulerGamma - 840 Log[2] + 420 Log[z])) z^8 + \[Ellipsis]) - ((Pi z^2)/16) (1 + z^4/216 + z^8/432000 + \[Ellipsis]) + ((Pi z^2)/32) (-2 + 4 EulerGamma - 4 Log[2] + 4 Log[z] + (1/864) (73 - 60 EulerGamma + 60 Log[2] - 60 Log[z]) z^4 + (7/204800) (-(4127/630) + 4 EulerGamma - 4 Log[2] + 4 Log[z]) z^8 + \[Ellipsis]) /; (z -> 0)








Standard Form





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MathML Form







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Rule Form





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





2007-05-02