On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
AuthorsLastra Sedano, Alberto; Huertas Cejudo, Edmundo José; Soria Lorente, Anier; Hermoso Ortíz, Carlos
IdentifiersPermanent link (URI): http://hdl.handle.net/10017/45707
Universidad de Alcalá
Hermoso, C., Huertas, E.J., Lastra, A. & Soria Lorente, A. 2020, “On second order q-difference equations satisfied by Al-Salam–Carlitz I-Sobolev type polynomials of higher order”, Mathematics, vol. 8, no. 8, 1300.
Al-Salam-Carlitz I polynomials
Al-Salam-Carlitz I-Sobolev type polynomials
Second order linear q-difference equations
Basic hypergeometric series
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
This contribution deals with the sequence fU(a)n (x; q, j)gn_0 of monic polynomials in x, orthogonal with respect to a Sobolev-type inner product related to the Al-Salam-Carlitz I ortogonal polynomials, and involving an arbitrary number j of q-derivatives on the two boundaries of the corresponding orthogonality interval, for some fixed real number q ϵ (0,1). We provide several versions of the corresponding connection formulas, ladder operators, and several versions of the second order q-difference equations satisfied by polynomials in this sequence. As a novel contribution to the literature, we provide certain three term recurrence formula with rational coefficients satisfied by U(a)n (x; q, j), which paves the way to establish an appealing generalization of the so-called J-fractions to the framework of Sobolev-type orthogonality.
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