In this chapter we prove various asymptotic results for special functions and classical orthogonal polynomials that have been stated without proof in previous chapters.
The method of proof used in the first three sections is to reduce the second-order differential equation to the point where it takes one of the following two forms:
a perturbation of the wave equation; or:
a perturbation of Bessel’s equation. In each case λ is a large parameter and one is interested in the asymptotic behavior of solutions as λ → +∞.
Taking into account ...