Asymptotic Chebyshev coefficients for two functions with very rapidly or very slowly divergent power series about one endpoint

Abstract

When a function is singular but infinitely differentiable at the origin, its power series diverges factorially and its Chebyshev coefficients are proportional to exp(-constant n^r) for 0 < r < 1. The two case studies presented here are novel by exemplifying the limits r → 0+ and r → 1−, respectively.