Chebyshev polynomials of the first kind and the univariate Lommel function: Integral representations

This study investigates a number of integrals possessing products of different indices of the univariate Lommel function, sμ,ν(a){s}_{\mu ,\nu }\left(a), with various elementary and special functions. As a consequence, connections between the function and Chebyshev polynomials of the first kind are established.