Balancing polynomials, Fibonacci numbers and some new series for π

07/13/2022

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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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Balancing polynomials, Fibonacci numbers and some new series for π

Gosper's algorithm and Bell numbers

Statistical thinking in simulation design: a continuing conversation on the balancing intercept problem

Tropical Laurent series, their tropical roots, and localization results for the eigenvalues of nonlinear matrix functions

The Lagrangian remainder of Taylor's series, distinguishes O(f(x)) time complexities to polynomials or not

Multidimensional Padé approximation of binomial functions: Equalities

Geographical Load Balancing across Green Datacenters

UMAP does not reproduce high-dimensional similarities due to negative sampling

Balancing polynomials, Fibonacci numbers and some new series for π

Related Research

Gosper's algorithm and Bell numbers

Statistical thinking in simulation design: a continuing conversation on the balancing intercept problem

Tropical Laurent series, their tropical roots, and localization results for the eigenvalues of nonlinear matrix functions

The Lagrangian remainder of Taylor's series, distinguishes O(f(x)) time complexities to polynomials or not

Multidimensional Padé approximation of binomial functions: Equalities

Geographical Load Balancing across Green Datacenters

UMAP does not reproduce high-dimensional similarities due to negative sampling