Abstract
In this paper we study the coefficients of an asymptotic expansion related to Somos' Quadratic Recurrence Constant. We develop recurrence relations and an asymptotic estimation for them. We also present some results which show that these coefficients are related to the Ordered Bell Numbers.
Highlights
Somos’ Quadratic Recurrence Constant, named after M
From (1) it can be shown that the generating function
The purpose of this paper is to develop recurrence relations and an asymptotic approximation for the ak’s
Summary
Somos’ Quadratic Recurrence Constant, named after M. Somos showed that gn has an asymptotic series as follows: (2) Where the first few coefficients ak are 1, 2, −1, 4, −21, 138, . From (1) it can be shown that the generating function A(x) = akxk k≥0 satisfies the functional equation
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