English

Balancing polynomials, Fibonacci numbers and some new series for $\pi$

Number Theory 2022-07-21 v1 Discrete Mathematics Combinatorics

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\pi involving Fibonacci and Lucas numbers. Our findings complement those of Castellanos from 1986 and 1989.

Keywords

Cite

@article{arxiv.2207.09451,
  title  = {Balancing polynomials, Fibonacci numbers and some new series for $\pi$},
  author = {Robert Frontczak and Kalika Prasad},
  journal= {arXiv preprint arXiv:2207.09451},
  year   = {2022}
}

Comments

16 pages, 5 tables