Hi
I am programming a problem for which I have to evaluate an expression of the form:
(R/g)J1(Rg) where J1(x) is a Bessel function.
I have to evaluate it at a range of "g" values including g = 0 which I believe gives me case of "0/0" as J1(0) = 0.
For other function where this occurs I have used L'Hopital but I don't know what to do for this case as I don't know how to differentiate the Bessel function.
Any help would be very much appreciated.
Yes I'm trying to find
In the limit where g goes to zero.
I know very little about Bessel functions myself other than they are the solutions of the bessel differential equation and that .
I'm using some numerical recipes code to calculate the Bessel function where g is non-zero.
You will find this reference to be fairly comprehensive. Look especially under "asymptotic relations."
I'm not going to bother to look it up in my references, but I believe there is also a recurrence relation you can use to find the slope as well.
-Dan