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BesselK






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselK[nu,z] > Series representations > Residue representations





http://functions.wolfram.com/03.04.06.0014.02









  


  










Input Form





BesselK[n, z] == (1/2) Sum[Residue[(Gamma[s + Abs[n]/2]/(z/2)^(2 s)) Gamma[s - Abs[n]/2], {s, Abs[n]/2 - j}], {j, 0, Abs[n] - 1}] + (1/2) Sum[Residue[(Gamma[s + Abs[n]/2] Gamma[s - Abs[n]/2])/(z/2)^(2 s), {s, -(Abs[n]/2) - j}], {j, 0, Infinity}] /; Element[n, Integers]










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