The Bessel Functions, Properties And Applications

ABSTRACT.

The Bessel's equation is a second order differential equation given as xv" +xy' + (x2- B)y=O Like most differential equations, it can be solved using various methods. This work makes use of the Frobenius method to arrive at a solution known as Bessel 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 physicists and engineers as they can be used to solve boundary value problems in mathematical physics and engineering.