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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 and a power function > Involving cosh and power > Linear arguments





http://functions.wolfram.com/03.04.21.0041.01









  


  










Input Form





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










Standard Form





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MathML Form







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</ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> </apply> </list> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29