%0 Journal Article 
%A Lastra Sedano, Alberto
%A Huertas Cejudo, Edmundo José
%A Soria Lorente, Anier
%A Hermoso Ortíz, Carlos
%T On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
%D 2020
%@ 2227-7390
%U http://hdl.handle.net/10017/45707
%X 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.
%K Al-Salam-Carlitz I polynomials
%K Al-Salam-Carlitz I-Sobolev type polynomials
%K Second order linear q-difference equations
%K Structure relations
%K Recurrence relations
%K Basic hypergeometric series
%K Matemáticas
%K Mathematics
%~ Biblioteca Universidad de Alcala