Pippenger, Nicholas An elementary approach to some analytic asymptotics. (English) Zbl 0828.26003 SIAM J. Math. Anal. 24, No. 5, 1361-1377 (1993). In J. Math. Anal. Appl. 48, 534-559 (1974; Zbl 0312.65091) M. L. Fredman and D. E. Knuth derived the asymptotic behaviour of sequences fulfilling conditions of the type \[ M(0)= 1,\;M(n+ 1)= \min_{0\leq k\leq n} (\alpha M(k)+ \beta M(n- k)) \] using the Wiener- Ikehara Tauberian theorem in the case where \(\log\alpha/\log \beta\) is irrational.In the present paper the author gives an elementary derivation that in the irrational case one only makes use of the fact that for irrational \(\vartheta\) the sequence \(n\vartheta\) is uniformly distributed modulo 1. Reviewer: P.Kirschenhofer (Wien) Cited in 3 Documents MSC: 26A12 Rate of growth of functions, orders of infinity, slowly varying functions 05A10 Factorials, binomial coefficients, combinatorial functions 05A16 Asymptotic enumeration 11B37 Recurrences Keywords:asymptotics of sequences Citations:Zbl 0312.65091 PDFBibTeX XMLCite \textit{N. Pippenger}, SIAM J. Math. Anal. 24, No. 5, 1361--1377 (1993; Zbl 0828.26003) Full Text: DOI Link