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BesselK






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselK[nu,z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving sinh > Linear arguments





http://functions.wolfram.com/03.04.21.0029.01









  


  










Input Form





Integrate[Sinh[a z] BesselK[\[Nu], a z], z] == (-(1/(-4 + \[Nu]^2))) (2^(-1 - \[Nu]) z (a z)^(1 - \[Nu]) ((2^(1 + 2 \[Nu]) Gamma[\[Nu]] + 4^\[Nu] Gamma[1 + \[Nu]]) HypergeometricPFQ[{3/4 - \[Nu]/2, 1 - \[Nu]/2, 5/4 - \[Nu]/2}, {3/2, 1 - \[Nu], 3/2 - \[Nu], 2 - \[Nu]/2}, a^2 z^2] + (a z)^(2 \[Nu]) (Gamma[1 - \[Nu]] + 2 Gamma[-\[Nu]]) HypergeometricPFQ[{3/4 + \[Nu]/2, 1 + \[Nu]/2, 5/4 + \[Nu]/2}, {3/2, 2 + \[Nu]/2, 1 + \[Nu], 3/2 + \[Nu]}, a^2 z^2]))










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