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# Methods and Applications of Analysis

## Volume 11 (2004)

### Number 2

### Orthogonal Polynomials Associated with Some Modification of a Linear Form

Pages: 267 – 294

DOI: http://dx.doi.org/10.4310/MAA.2004.v11.n2.a6

#### Authors

#### Abstract

We show that if *v* is a regular Laguerre-Hahn (resp. semiclassical) linear form,then the linear form *u* defined by the relation LAMBDA(*x - a *)*u* = (*x - c*)*v* is also regular and a Laguerre-Hahn (resp. semiclassical) linear form for every complex LAMBDA except for a discrete set of numbers depending on *v, a*, and *c*. We give explicitly the coefficients of the three-term recurrence relation, the structure relation of the orthogonal sequence associated with u, and the class of the linear form *u* knowing that of *v*. Finally, we apply the above results to some examples.