  We describe a family of polynomials discovered via a particular recursion
relation, which have connections to Chebyshev polynomials of the first and the
second kind, and the polynomial version of Pell's equation. Many of their
properties are listed in Section 3. We show that these families of polynomials
in the variable $t$ satisfy certain second order linear differential equations
that may be of interest to mathematicians in conformal field theory and number
theory. We also prove that these families of polynomials in the setting of
Date-Jimbo-Kashiwara-Miwa algebras when multiplied by a suitable power of $t$
are orthogonal with respect to explicitly-described kernels. Particular cases
lead to new identities of elliptic integrals (see Section 5).
