Bessel Function And The Modified Bessel Function

Bessel function is defied for a first time by the mathematician Daniel Bernoulli and generalized by Friedrich Bessel. Bessel functions are also called cylinder function or cylindrical harmonic function because they are found in the solution to Laplaces equation in cylindrical coordinated. Bessel equation arises in problems involving vibrations, or heat conduction in regions possessing circular symmetry; therefore Bessel function have many application in physics and engineering in connection with the propagation of waves, elasticity, fluid motion and especially in many problem of potential theory and diffusion involving cylindrical symmetry. This work consists three chapters. The first chapter remained about the power series, second order linear differential equation, singularity point, Sturm-Liouville problem and then gamma function which help to express factorial. In the second chapter it is discussed about the Bessel equation and its solution which is Bessel functions with the plot of Bessel function. The third chapter discuss about the modified Bessel equation and its solution, which is the special case of the Bessel equation.