Thread: 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.

It would help if we had the attachment

CB

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.