Connection coefficients for orthogonal polynomials: symbolic computations, verifications and demonstrations in the Mathematica language

We deal with the problem of obtaining closed formulas for the connection coefficients between orthogonal polynomial sequences and, also, the canonical sequence, using a recursive methodology based on symbolic computations, verifications and demonstrations in the Mathematica ^® language. We present the corresponding software that is available in Netlib and, with it, we derive new formulas for the connection coefficients for some semi‐classical of class 1 families.