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**A family of singular semi-classical functionals.**
*(English)*
Zbl 1031.42025

The distributional equation of a semi-classical functional provides an efficient way to study the properties of the semi-classical OPS/functionals. A particular case of semi-classical OPS/functionals are the classical ones. For the distributional equation of classical functionals a regularity condition holds. The main result of the present paper is to show that in general such condition does not hold. The examples of semi-classical functionals that satisfy certains singular equation are built and an explicit representation of the corresponding monic orthogonal polynomials as well as the recurrence relations are found.

Reviewer: Leonid Golinskii (Kharkov)

### MSC:

42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |

33E30 | Other functions coming from differential, difference and integral equations |

### Keywords:

semi-classical functionals; distributional equation; quasi-orthogonality; regularity condition; admissibility condition; orthogonal polynomials### References:

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