# Differentiating Bessel funtion

• Jun 18th 2008, 05:44 AM
jbd
Differentiating Bessel funtion
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.
• Jun 18th 2008, 05:51 AM
colby2152
Quote:

Originally Posted by jbd
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.

Can you describe the Bessel function to those who are not familiar with it?

Are you trying to find the domain of $\displaystyle f(g)=\frac{R}{g}J_1(Rg)$?
• Jun 18th 2008, 06:04 AM
jbd
Yes I'm trying to find
$\displaystyle f(g)=\frac{R}{g}J_1(Rg)$

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 $\displaystyle J_1(0)=0$.

I'm using some numerical recipes code to calculate the Bessel function where g is non-zero.

• Jun 18th 2008, 08:01 AM
topsquark
Quote:

Originally Posted by jbd
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.

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
• Jun 18th 2008, 08:18 AM
jbd
Thank you.