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BesselK






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselK[nu,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > Logarithmic cases





http://functions.wolfram.com/03.04.06.0036.01









  


  










Input Form





BesselK[n, z] \[Proportional] (((n - 1)!/2) (1 - (1/(4 (n - 1))) z^2 + (1/(32 (n - 1) (n - 2))) z^4 + \[Ellipsis]))/(z/2)^n + ((-1)^(n - 1)/n!) Log[z/2] (z/2)^n (1 + z^2/(4 (n + 1)) + z^4/(32 (n + 1) (n + 2)) + \[Ellipsis]) + (((-1)^n 2^(-1 - n) z^n)/n!) (-EulerGamma + PolyGamma[1 + n] + ((1 - EulerGamma + PolyGamma[2 + n])/(4 (n + 1))) z^2 + ((3/2 - EulerGamma + PolyGamma[3 + n])/(32 (n + 1) (n + 2))) z^4 + \[Ellipsis]) /; (z -> 0) && Element[n - 3, Integers] && n - 3 >= 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





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