A Class of Non-Symmetric Semi-Classical Linear Forms

Zaatra Mohamed

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.


Keywords


Keywords: Orthogonal polynomials; Semi-classical linear forms; Integral rep-resentation; Structure relation.

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References


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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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