Properties of two Chebyshev-like polynomial sequences

By modifying the generating function of the Chebyshev polynomials of the second kind, we obtain a sequence of reciprocal (or palindromic) polynomials, as well as a related companion sequence.

Among numerous other properties, we obtain discriminant and resultant identities for these polynomial sequences and prove partial irreducibility results.

Throughout, we point to parallels and connections with the Chebyshev polynomials of both kinds.