Hypergeometric connections between balancing polynomials and Chebyshev polynomials of first and second kinds

Abstract

In the present study, we find several connections between balancing polynomials and the Chebyshev polynomials of the first and second kinds. The Chebyshev polynomials of the first and second kinds are expressed as the sum of two terms of balancing polynomials with hypergeometric coefficients. As an inversion, the balancing polynomials are also expressed as the sum of two terms of the Chebyshev polynomials of the first kind and the Chebyshev polynomials of the second kind with hypergeometric coefficients.