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BesselI




Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselI[nu,z] > Series representations > Asymptotic series expansions > Expansions for any z in trigonometric form > Using trigonometric functions with branch cut-free arguments





http://functions.wolfram.com/03.02.06.0083.01









  


  








Input Form





BesselI[\[Nu], z] \[Proportional] (z^\[Nu]/((I z)^\[Nu] Sqrt[2 Pi])) (((E^(I Pi \[Nu])/Sqrt[(-I) z]) (1 + Sqrt[z^2]/z) Cosh[z - (I Pi (1 + 2 \[Nu]))/4] + (1/Sqrt[I z]) (1 - Sqrt[z^2]/z) Cosh[z + (I Pi (1 + 2 \[Nu]))/4]) (Sum[(Pochhammer[(1 - 2 \[Nu])/4, k] Pochhammer[(3 - 2 \[Nu])/4, k] Pochhammer[(1 + 2 \[Nu])/4, k] Pochhammer[(3 + 2 \[Nu])/4, k])/ (Pochhammer[1/2, k] k! z^(2 k)), {k, 0, n}] + O[1/z^(2 n + 2)]) + ((1 - 4 \[Nu]^2)/(8 z)) ((E^(I Pi \[Nu])/Sqrt[(-I) z]) (1 + Sqrt[z^2]/z) Sinh[z - (I Pi (1 + 2 \[Nu]))/4] + (1/Sqrt[I z]) (1 - Sqrt[z^2]/z) Sinh[z + (I Pi (1 + 2 \[Nu]))/4]) (Sum[(Pochhammer[(3 - 2 \[Nu])/4, k] Pochhammer[(5 - 2 \[Nu])/4, k] Pochhammer[(3 + 2 \[Nu])/4, k] Pochhammer[(5 + 2 \[Nu])/4, k])/ (Pochhammer[3/2, k] k! z^(2 k)), {k, 0, n}] + O[1/z^(2 n + 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