Analysis Of The Bessel Functions

ABSTRACT

 As a special function and a second order differential equation, the Bessel equation is of the form. x?y" + xy'+ (x?-v?) y= 0 Considering the method of solution, this work deploys the Frobenius method in getting a solution known as the Bessel functions. The relationship between the Gamma function and the Bessel function, emphasis on infinite series and improper integral in relation to Bessel and Gamma functions were considered. The zeros on the Bessel function, the modified Bessel function which allows treatment using complex variables were also considered. Finally, we considered a special and concise way of solving Bessel's differential equation and other differential equation that can be reduced to Bessel's differential equation, hence, the Bessel function as a solution.