Continued fractions and Stern polynomials

By using specific subsequences of two different types of generalized Stern polynomials, we obtain several related classes of finite and infinite continued fractions involving a single term z t j in their partial numerators, where z is a complex variable and t is a positive integer. This approach is...

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Bibliographic Details
Published in:The Ramanujan journal 2018-04, Vol.45 (3), p.659-681
Main Authors: Dilcher, Karl, Ericksen, Larry
Format: Article
Language:English
Subjects:
Combinatorics
Complex variables
Field Theory and Polynomials
Fourier Analysis
Functions (mathematics)
Functions of a Complex Variable
Mathematical analysis
Mathematics
Mathematics and Statistics
Number Theory
Polynomials
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Summary:By using specific subsequences of two different types of generalized Stern polynomials, we obtain several related classes of finite and infinite continued fractions involving a single term z t j in their partial numerators, where z is a complex variable and t is a positive integer. This approach is extended to other, sparser, subsequences of Stern polynomials, based on certain Lucas functions; this then leads to further infinite classes of continued fractions.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-016-9864-3