RT info:eu-repo/semantics/article
T1 On second order q-difference equations satisfied by Al-Salam-Carlitz I-Sobolev type polynomials of higher order
A1 Lastra Sedano, Alberto
A1 Huertas Cejudo, Edmundo José
A1 Soria Lorente, Anier
A1 Hermoso Ortíz, Carlos
K1 Al-Salam-Carlitz I polynomials
K1 Al-Salam-Carlitz I-Sobolev type polynomials
K1 Second order linear q-difference equations
K1 Structure relations
K1 Recurrence relations
K1 Basic hypergeometric series
K1 Matemáticas
K1 Mathematics
AB 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 theAl-Salam-Carlitz I ortogonal polynomials, and involving an arbitrary number j ofq-derivativeson the two boundaries of the corresponding orthogonality interval, for somefixed real number q ϵ (0,1). We provide several versions of the corresponding connection formulas, ladderoperators, and several versions of the second order q-differenceequations satisfied by polynomials in this sequence. As a novel contribution tothe literature, we provide certain three term recurrence formula with rationalcoefficients satisfied by U(a)n(x; q, j),which paves the way to establish an appealing generalization of the so-called J-fractionsto the framework of Sobolev-type orthogonality.
PB MDPI
SN 2227-7390
YR 2020
FD 2020-08-06
LK http://hdl.handle.net/10017/45707
UL http://hdl.handle.net/10017/45707
LA eng
NO Universidad de Alcalá
DS MINDS@UW
RD 28-abr-2024