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

Authors:
Pascal Maroni;Zélia Rocha
Affiliations:
Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie - CNRS, Paris cedex 05, France 75252;Departamento de Matemática, Faculdade de Ciências da Universidade do Porto - CMUP, Porto, Portugal 4169-007
Venue:
Numerical Algorithms
Year:
2013

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Abstract

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.