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# Question: How to find the roots of Bessel's function between -4 and 4 using the newton raphson method in maple?

March 20 2013 by
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Hi, I am having a little trouble finding the roots of Bessel's function J0 between -4 and 4 using the newton Raphson method, the main issue I am having is not knowing what to input at a certain point.

f:=x->x-evalf(cos(x));                     f := x -> x - evalf(cos(x))> low:=-10;                              low := -10> up:=10;                               up := 10> step:=1;                              step := 1> > dp:=5;                               dp := 5> > for i from low to up-step by step do> >           a:=i:>           b:=i+step: >               >      if f(a)*f(b) < 0 then           > >          print(root in interval,a,b):>                 >      fi:> > od:                         root in interval, 0, 1
As you can see above I was able to get maple to find me the root interval,

How would I do the same for Bessel's function? What would I put into f:=