any order of the orthogonal polynomials, namely, Chebyshev polynomials of the sixth kind in
terms of Chebyshev polynomials themselves. We will prove that these expressions involve
certain terminating hypergeometric functions of the type 4 F 3 (1) that can be reduced in
some specific cases. The derived expressions along with the linearization formula of
Chebyshev polynomials of the sixth kind serve in obtaining a numerical solution of the non …