Question: BesselJ&BesselY BesselI&BesselK

March 10 2010 lei_xiaowen 269
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In the help, it writes

BesselJ and BesselY are the Bessel functions of the first and second kinds, respectively. They satisfy Bessel's equation:
     2                2    2
    x  y'' + x y' + (x  - v ) y = 0
 

BesselI and BesselK are the modified Bessel functions of the first and second kinds, respectively. They satisfy the modified Bessel equation:
     2                2    2
    x  y'' + x y' - (x  + v ) y = 0
 

HankelH1 and HankelH2 are the Hankel functions, also known as the Bessel functions of the third kind. They also satisfy Bessel's equation, and are related to BesselJ and BesselY by
    HankelH1(v,x) = BesselJ(v,x) + I*BesselY(v,x)
    HankelH2(v,x) = BesselJ(v,x) - I*BesselY(v,x)
 

What is the differents bewteen BesselJ&BesselY ,BesselI&BesselK?

In what condition I can use BesselJ or BesselY , BesselI&BesselK?

Thank you

 

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