Expansion in Series of Bessel Functions and Transmutations for Perturbed Bessel Operators

A. Fitouhi and M. M. Hamza (SIAM J. Math. Anal. 21, No. 6, 1990, 1619-1632) obtained an expansion in series of Bessel functions for eigenfunctions of second-order differential operators, these series being uniformly convergent on (0, γ). In this paper, we give first a new proof of this result leading to a large domain of uniform convergence, and then study a transmutation operator between two classes of perturbed Bessel operators.