The rate of convergence of Hermite function series

John P. Boyd
1980 Mathematics of Computation  
Let a > 0 be the least upper bound of y for which f(z) -0(e-°My) for some positive constant q as |z| -+ o» on the real axis. It is then proved that at least an infinite subsequence of the coefficients \an} in oo f(z) = e-z2/2 £ anHn(z), n=0
doi:10.1090/s0025-5718-1980-0583508-3 fatcat:jceqypjw5bfxndktt4lablytmm