University of Calgary

Stern poynomials, Fibonacci numbers, and continued fractions

Submitted by ccameron on Tue, 05/29/2012 - 10:05am.
Jun 5 2012 - 3:00pm

Karl Dilcher, Dalhousie University

MS 431

We derive new identities for a polynomial analogue of the Stern sequence and define two subsequences of these polynomials. We obtain various properties for these two interrelated subsequences which have 0-1 coefficients and can be seen as extensions or analogues of the Fibonacci numbers. We also define two analytic functions as limits of these sequences.

As an application we obtain evaluations of certain finite and infinite continued fractions whose partial quotients are doubly exponential. In a case of particular interest, the set of convergents has exactly two limit points. (Joint work with K.B. Stolarsky).