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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/03.04.06.0006.01









  


  










Input Form





BesselK[n, z] == ((-1)^n/8) ((-((2^(4 - n) z^(-2 + n))/(n - 1)!)) HypergeometricPFQ[{1, 1, 1 - n}, {}, 4/z^2] + (z^(2 + n)/(2^n ((1 + n) (1 + n)!))) ((1 + n) HypergeometricPFQ[{{}, {1}, {1, 1}}, {{2, 2 + n}, {}, {2}}, z^2/4, z^2/4] + HypergeometricPFQ[{{}, {1}, {1, 1 + n}}, {{2, 2 + n}, {}, {2 + n}}, z^2/4, z^2/4]) - 4 BesselI[n, z] (EulerGamma + 2 Log[z/2] - PolyGamma[1 + n])) /; Element[n, Integers] && n >= 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)





2001-10-29





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