An approach to obtaining identities with binomial coefficients and orthogonal polynomials

A series of new combinatorial identities with binomial coefficients and orthogonal polynomials is obtained by using a unified approach. These identities contain Hermite polynomials, Legendre polynomials, Chebyshev polynomials of the first and second kind, Gegenbauer polynomials, and Krawtchouk polynomials.