The Bessel's Function, Properties And Applications

ABSTRACT

The Bessel equation is a second order differential equation given as xy + xy' + (x2- v)y = 0 Like most differential equationit can be solved using various methods. This work makes use of the method of Frobenius to arrive at a solution known as Bessel's functions. Furthermore, these functions have recurrence relations and can be modified to accommodate treatment using complex variables. They also have roots called " Zeros" which have the properties of being simple and infinitely many. The roots of Bessel's functions of different orders interlace. Finally, these functions are of immense importance to physicist and engineers as they can be used to solve boundary value problems in mathematical physics and I engineering.