د.الفيتوري محمد سالم عمر2024-12-182024-12-18https://dspace.academy.edu.ly/handle/123456789/931The Bessel differential equation is a homogeneous linear differential equation of the second order with variable coefficients, and it has two linearly independent solutions, which called Bessel functions. This thesis dealt with the Bessel differential equation, the origin of the equation and the method of solving it using Frobenius series explained, then we discussed Bessel functions of first kind, the recurrence relations, and the generated function with their representation in an integral formula.The Bessel differential equation is a homogeneous linear differential equation of the second order with variable coefficients, and it has two linearly independent solutions, which called Bessel functions. This thesis dealt with the Bessel differential equation, the origin of the equation and the method of solving it using Frobenius series explained, then we discussed Bessel functions of first kind, the recurrence relations, and the generated function with their representation in an integral formula.Definite and Improper Integrals