Identities for squared central binomial coefficients

TL;DR

This paper proves four identities involving squared central binomial coefficients, linking them to elliptic integrals and Lagrange polynomial properties, enhancing understanding of their mathematical structure.

Contribution

It introduces four new identities for squared central binomial coefficients, connecting them to elliptic integrals and polynomial properties, which were previously unexplored.

Findings

Four identities for squared central binomial coefficients are established.

Three identities relate to transformation properties of elliptic integrals.

One identity is based on properties of Lagrange polynomials.

Abstract

We prove four identities for the squared central binomial coefficients. The first three of them reflect certain transformation properties of the complete elliptic integrals of the first and the second kind, while the last one is based on properties of the Lagrange polynomials.