Re: solution
- To: mathgroup at smc.vnet.net
- Subject: [mg118281] Re: solution
- From: Peter Pein <petsie at dordos.net>
- Date: Wed, 20 Apr 2011 04:27:07 -0400 (EDT)
- References: <iojpp7$i52$1@smc.vnet.net>
Am 19.04.2011 12:56, schrieb amelia Jackson:
> 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...
Indeed the roots are asyptotically at (k+1/4) Pi for k->Infinity:
Limit[Abs[f[Pi*(k + 1/4)]] Sqrt[k], k -> Infinity,
Assumptions -> Element[k, Integers]]
11/(4 Sqrt[2] \[Pi])
so Abs[f[Pi*(k + 1/4)]] ~ k^(-1/2)
leading to the much easier table of roots:
In[118]:= Length[
zeros=Union[Table[x/. FindRoot[f[x],{x,(k+1/4) Pi}], {k,100}],
SameTest->(Abs[#1-#2]<=1&)]]
Take[zeros,-3]
Out[118]= 100
Out[119]= {308.657,311.799,314.94}