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Continued fractions and Stern polynomials

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Abstract

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.

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Correspondence to Karl Dilcher.

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Research supported in part by the Natural Sciences and Engineering Research Council of Canada, Grant # 145628481.

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Dilcher, K., Ericksen, L. Continued fractions and Stern polynomials. Ramanujan J 45, 659–681 (2018). https://doi.org/10.1007/s11139-016-9864-3

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  • DOI: https://doi.org/10.1007/s11139-016-9864-3

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