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Math Help - Bessel functions of the first order and zero order.

  1. #1
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    Bessel functions of the first order and zero order.

    Hi Guys,

    So I'm in no rush to get this question answered but I am certainly struggling trying to wrap my head around this problem.

    The Background
    ----------------
    I'll be performing a FRAP experiment as a means to measure a diffusion coefficient. The model I'll be using to determine the tracer diffusion coefficient is the following:

    Attachment 18686

    Solving this equation will likely be done through Matlab or VBA using a least squares fitting procedure. My issue stems from the two Bessel functions in the equation. I've done some research into them and I can honestly say I'm stumped as to what they are and how to approach a solution to them.

    To simplify my question:
    ------------------------

    How would one approach a least square fitting procedure to this equation? The Bessel functions are primarily throwing me off. Perhaps there is a simplification which can make my work easier?

    The experimental data will output the fluorescence intensity with respect to time. My objective is to find TD, the characteristic diffusion time.
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  2. #2
    Grand Panjandrum
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    It would help if we had the attachment

    CB
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  3. #3
    A Plied Mathematician
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    Without the attachment, as CB said, I can only go from my previous experience. The Bessel functions are defined using an infinite series. That's not usually suitable to work with in a numerical scheme like least squares. I would truncate the series after, say, 20 terms or so, and use that instead.
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