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Math Help - Simplifying a ratio of modified Bessel functions of the second kind

  1. #1
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    Simplifying a ratio of modified Bessel functions of the second kind

    I found the following solution to a differential equation problem but need to simplify it:

    K0(A*x)/K0(A*B)

    where K0 is the modified Bessel function of the second kind with alpha = 0, x is the independent variable, and A and B are constants. I'm only interested in the interval x>=B.

    So far, I've tried to use the definitions of the Bessel functions to replace K0s with I0s with J0s, or K0s with H0s with J0s, but I frequently wind up with zeroes top and bottom. Any tips or solutions?
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  2. #2
    Grand Panjandrum
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    Re: Simplifying a ratio of modified Bessel functions of the second kind

    Quote Originally Posted by penguinick View Post
    I found the following solution to a differential equation problem but need to simplify it:

    K0(A*x)/K0(A*B)

    where K0 is the modified Bessel function of the second kind with alpha = 0, x is the independent variable, and A and B are constants. I'm only interested in the interval x>=B.

    So far, I've tried to use the definitions of the Bessel functions to replace K0s with I0s with J0s, or K0s with H0s with J0s, but I frequently wind up with zeroes top and bottom. Any tips or solutions?
    If A and B are arbitrary constants in the solution, then set C=1/K_0(A \times B) then you have C \; K_0(Ax)

    CB
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  3. #3
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    Re: Simplifying a ratio of modified Bessel functions of the second kind

    Quote Originally Posted by CaptainBlack View Post
    If A and B are arbitrary constants in the solution, then set C=1/K_0(A \times B) then you have C \; K_0(Ax)

    CB
    Nice... but there's no way to reduce it into something that doesn't have infinite series, I take it?
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