Summary: Structure relations for orthogonal polynomials with respect to Hermitian linear functionals are studied. Firstly, we prove that semi-classical orthogonal polynomials satisfy structure relations of the following type:
where are integers (specified in the text), is the reversed polynomial of , and are complex numbers. Then, we study the semi-classical character of sequences of orthogonal polynomials , connected through a structure relation of the following type:
where the integers satisfy some natural conditions specified in the text.