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arXiv · 2207.09451

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

Robert Frontczak·Kalika Prasad
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Abstract

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 $π$ involving Fibonacci and Lucas numbers. Our findings complement those of Castellanos from 1986 and 1989.

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Robert Frontczak, Kalika Prasad. 2022-07-13. Balancing polynomials, Fibonacci numbers and some new series for $π$. https://arxiv.org/abs/2207.09451

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