1. Bessel functions.
For this activity you will need the Bessel function of the first kind of order 1, known to Maple as BesselJ(1,x), which is defined by
Hence we have
(a) Find the domain of , i.e. what is the radius of convergence?
(b) Graph the first several partial sums (use and of the Bessel function along with itself on the
same coordinate axes. Use the viewing window [ ] by [ ] .
2. More Bessel functions.
The Bessel function of the first kind of order 0 is given by
Maple knows this function as . That is we can define this function by
(a) Show that J satisfies the differential equation:
(b) Evaluate correct to three dedcimal places.