Gamma, Beta and error functions. Bessel functions of first and second kind. Linear independence and recurrence relations. Calculation of integrals involving Bessel functions. Modified Bessel functions of first and second kind. Solving some types of Ordinary Differential Equations using Bessel functions. Lommel’s integrals. Some results about the zeros of Bessel functions. Fourier-Bessel series. General properties of orthogonal polynomials. Three term recurrence relation. Darboux-Christoffel formula. Rodrigue’s formula. Generating functions. Applications.