Closed Form Continued Fraction Expansions of Special Quadratic Irrationals | Zendy

Daniel Fishman | Zendy; Steven J. Miller | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Closed Form Continued Fraction Expansions of Special Quadratic Irrationals

Author(s) -

Daniel Fishman,

Steven J. Miller

Publication year - 2013

Publication title -

isrn combinatorics

Language(s) - English

Resource type - Journals

ISSN - 2090-8911

DOI - 10.1155/2013/414623

Subject(s) - fibonacci number , mathematics , continued fraction , fraction (chemistry) , integer (computer science) , quadratic equation , recurrence relation , simple (philosophy) , relation (database) , combinatorics , quadratic form (statistics) , pure mathematics , arithmetic , remainder , computer science , geometry , chemistry , organic chemistry , epistemology , database , philosophy , programming language

We derive closed form expressions for the continued fractions of powers of certain quadratic surds. Specifically, consider the recurrence relation with , , a positive integer, and (note that gives the Fibonacci numbers). Let . We find simple closed form continued fraction expansions for for any integer by exploiting elementary properties of the recurrence relation and continued fractions.

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research