Discrete polynomials orthogonal with respect Sobolev-type inner product associated with Chebyshev polynomials orthogonal on a uniform grid

In current paper we consider new polynomials, generated by orthogonal on uniform grid Chebyshev polynomials. Newly introduced polynomials are themselves orthogonal with respect to the Sobolev-type inner product. The explicit form of these polynomials, convenient to study their asymptotic properties, is obtained.