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arXiv:2207.09451 [math.NT]AbstractReferencesReviewsResources

Balancing polynomials, Fibonacci numbers and some new series for $π$

Robert Frontczak, Kalika Prasad

Published 2022-07-13Version 1

We evaluate some types of infinite series with balancing and Lucas-balancing polynomials in closed form. These evaluations will lead to some new curious series for $\pi$ involving Fibonacci and Lucas numbers. Our findings complement those of Castellanos from 1986 and 1989.

Comments: 16 pages, 5 tables
Categories: math.NT, cs.DM, math.CO
Subjects: 11B37, 11B39, 15A15
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