Re: solution
- To: mathgroup at smc.vnet.net
- Subject: [mg118282] Re: solution
- From: Heike Gramberg <heike.gramberg at gmail.com>
- Date: Wed, 20 Apr 2011 04:27:18 -0400 (EDT)
According to my trusty copy of Abramowitz and Stegun, BesselJ[a,k] tends to Sqrt[2/Pi/k] Cos[k-a Pi/2-Pi/4] for
k large (where large is about k>3 for a=1), so your function behaves as
BesselJ[0,k]+k BesselJ[1,k] -> Sqrt[2 k/Pi] Cos[k-Pi/2-Pi/4]
plus something of order O(1/Sqrt[k]) for k>3. Therefore, the zeros will be at approximately k=Pi/4 + m Pi,
where m is a positive integer (so you're right that they are approximately Pi apart).
To get the zeros you want, you can therefore do something like
r = Table[
k /. FindRoot[BesselJ[0, k] + k BesselJ[1, k] = 0, {k, n}], {n, Pi/4 + Pi Range[100]}]
Heike
> BesselJ[0, k] + k BesselJ[1, k]
On 19 Apr 2011, at 11:56, amelia Jackson wrote:
> Dear MathGroup,
>
> I have a problem. I want to find solution:
> r := Table[
> k /. FindRoot[BesselJ[0, k] + k BesselJ[1, k] = 0, {k, n}], {n, 1, 100}]
>
> but I get about 30 roots. I need about 100 or more.
> I think that "step" "n" tend to Pi
>
> Please for help...