Some Basic Line-sequential Properties of Polynomial Line-sequences

There have been many reports on the properties of various polynomial sequences and their generalizations (see, e.g., [1], [3], [4], [5], [6], and [9] and the references therein). In this paper we shall try to treat some polynomial sequences by virtue of the line-sequential formalism developed earlier. To this end? we choose [9] as the guide of our endeavor and obtain some results of a different variety supplementary to those appearing in the literature. In particular, we treat the Morgan-Voyce (MV) polynomial sequences in some detail (for the origination of the MV polynomials, see the references in [1]) and then apply the method to the Jacobsthal (J) and the Vieta (V) polynomial sequences. Finally, we illustrate applications of these results with some examples. The line-sequential treatments of at least some of the other well-known polynomial sequences are somewhat more complicated, so these and other related matters will be discussed in a later report.