On the general cubic decomposition of polynomial sequences

Symbolic approach to the general cubic decomposition of polynomial sequences. Results for several orthogonal and symmetric cases

“…These properties, not yet proven for all n, can be the object of posterior theoretical studies that are out of the scope of this work. For instance, the CD of an orthogonal MPS where {a 2 n } n≥0 and {b 2 n } n≥0 vanish can be studied analogously to the case where a 1 n = a 2 n = 0, n ≥ 0, which is treated in [9], although with an increase in technical difficulties. Results due to Theorem 3.1 Results fulfilled for n = 0, .…”

“…Then, the coefficients of Theorem 1.3 of [9], for all parameters a, b, c, p, q and r are the following.…”

“…Theorem 2.4 of reference [9] characterizes the component sequences of a CD of {W n } n≥0 in terms of its structure coefficients and it is enunciated as follows.…”

“…In [9] the most general cubic decomposition of a given MPS was presented. Indeed, fixing a monic cubic polynomial…”

“…The most general cubic decomposition (CD) of a monic polynomial sequence (MPS) was presented recently in [9,12] and constitutes a complete polynomial CD of a given MPS. In this last reference, the reader can find extensive information and a bibliography about this subject.…”