A general method for deriving some semi-classical properties of perturbed second degree forms: The case of the Chebyshev form of second kind

We present a new general method and the corresponding symbolic algorithm PSDF for deriving some semi-classical properties of perturbed second degree forms namely: the Stieltjes function, the Stieltjes equation, the functional equation, the class, a structure relation and the second order linear differential equation. We give new explicit results for some perturbed of order 3 of the second kind Chebyshev polynomials.