Orthogonal polynomials via random variables (Q2895371)

Orthogonal polynomials can be generated in different ways, all of which are based on the associated measure. For instance, one can use the Gram-Schmidt procedure or the three-term recurrence relation. The authors study a random variable that is generated by a finite probability measure. Then three different ways of generating orthonormal polynomials in this random variable are compared. They argue that the best way is a particular central version of the Gram-Schmidt procedure. Explicit formulas are given for the first six polynomials generated by this random variable. Moreover, recurrence formulas are obtained for the general polynomials.