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BesselI






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselI[nu,z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving cosh > Power arguments





http://functions.wolfram.com/03.02.21.0035.01









  


  










Input Form





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










Standard Form





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MathML Form







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</ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <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> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> </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





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