Progress in Applied Mathematics
A Class of Non-Symmetric Semi-Classical Linear Forms
Abstract
We show that if v is a regular semi-classical form (linear functional), then the form u defined by (x − τ 2 )σu = −λv and σ(x − τ )u = 0 where σu is the even part of u, is also regular and semi-classical form for every complex λ except for a discrete set of numbers depending on v. We give explicitly the recurrence coefficients and the structure relation coefficients of the orthogonal polynomials sequence associated with u and the class of the form u knowing that of v. We conclude with illustrative examples.
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DOI: http://dx.doi.org/10.3968/4630
DOI (PDF): http://dx.doi.org/10.3968/pdf_10
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