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BesselI






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselI[nu,z] > Series representations > Asymptotic series expansions > Expansions inside Stokes sectors > Expansions containing z->infinity > In hyperbolic form ||| In hyperbolic form





http://functions.wolfram.com/03.02.06.0065.01









  


  










Input Form





BesselI[\[Nu], z] \[Proportional] ((Sqrt[2]/Sqrt[Pi z]) (Cosh[z + (Pi I (2 \[Nu] + 1))/4] HypergeometricPFQ[{(1 - 2 \[Nu])/4, (3 - 2 \[Nu])/4, (1 + 2 \[Nu])/4, (3 + 2 \[Nu])/4}, {1/2}, 1/z^2] + ((1 - 4 \[Nu]^2)/(8 z)) Sinh[z + (Pi I (2 \[Nu] + 1))/4] HypergeometricPFQ[ {(3 - 2 \[Nu])/4, (5 - 2 \[Nu])/4, (3 + 2 \[Nu])/4, (5 + 2 \[Nu])/4}, {3/2}, 1/z^2]))/E^((Pi I (2 \[Nu] + 1))/4) /; -Pi < Arg[z] < Pi/2 && (Abs[z] -> Infinity)










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)





2007-05-02





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