Abstract
We define the family of truncated Hermite polynomials , orthogonal with respect to the linear functional The connection of with Hermite and Rys polynomials is stated. The semiclassical character of as polynomials of class 2 is emphasized. As a consequence, several properties of concerning the coefficients in the three-term recurrence relation they satisfy as well as the moments and the Stieltjes function of L are given. Ladder operators associated with such a linear functional and the holonomic equation that the polynomials satisfy are deduced.
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