Balancing polynomials, Fibonacci numbers and some new series for π
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.