The Coefficients in an Asymptotic Expansion
L. Carlitz · Proceedings of the American Mathematical Society · 1965
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 j 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 Aiäl, Sniz) = Ë (-) Uriz) + Oin-") r=o \ n /