The coefficients in an asymptotic expansion

Put " (z)r inz)ne"=Tl-j-+-^Saiz), r=o r\ n\ where is a positive integer and z an arbitrary complex number.Ramanujan [4, p. 26] asserted (in a different notation) that n\/e 2 4 /1\ 5.(1) = -( -)-+-+ 0( -) 2 3 135 2/Copson [2] proved that {5"( -1)} is a decreasing sequence with limit -1/2 and derived an asymptotic series.In a recent paper, Buckholtz [l] proved that, for Ail, Sniz) = (-) Uriz) + Oin-") r=o \ n /