Re: Roots of Bessel first kind function

[Rob Mahurin]

On May 23, 2009, at 8:58 AM, Adrian Spiridon wrote:
>         I want to find the firs "s" roots of the function J(alpha,  
> z) - Bessel's first kind function. Suppose alpha=0 , the first 3
> roots are: z1=2.4048, z2=5.5201, z3= 8.6537.
>         I  have defined  f=@(x)besselj(0,x) and I've tried to use  
> the function fzero but this isn't a viable solution
> because fzero needs an interval in wich to search for the root, and  
> at the ends of the interval f must have different signes.
>         Because I don't know how fast the roots may succed,or what  
> the sign of the function is,  I am unable to use fzero function.

See eq. 58 of
        http://mathworld.wolfram.com/BesselFunctionoftheFirstKind.html
for the asymptotic form.  This gives you a good starting guess for  
the location of the zeros at large argument.

>         Is there any built-in function that can find the zeros of   
> Bessels's first kind function ? If not (I guess not), how can I
> find the roots ?


If you know the roots are separated by roughly pi, fzero will work.

Cheers,
Rob

--
Rob Mahurin
Department of Physics and Astronomy
University of Tennessee                 865 207 2594
Knoxville, TN 37996                     address@hidden