Expansion in terms of Gegenbauer polynomials for solutions of a perturbed Gegenbauer differential equation

A. Fitouhi and M.M. Hamza (SIAM J. Math., No. 6 (1990) 1619-1632) and with H. Chebli (JMMA, Vol. 181, No. 3(1994) 789-802) obtained Bessel functions series expansions for the eigenfunctions of certain second order differential operators. This paper uses the same basic method to show that solutions of the perturbed Gegenbauer differential equation with an initial condition expand as a uniformly convergent Gegenbauer polynomial series on an interval.