Named essentially after their close relationship with the modified Bessel function Ksub.ν(z) of the second kind, which is known also as the Macdonald function (or, with a slightly different ...definition, the Basset function), the so-called Bessel polynomials ysub.n(x) and the generalized Bessel polynomials ysub.n(x;α,β) stemmed naturally in some systematic investigations of the classical wave equation in spherical polar coordinates. Our main purpose in this invited survey-cum-expository review article is to present an introductory overview of the Bessel polynomials ysub.n(x) and the generalized Bessel polynomials ysub.n(x;α,β) involving the asymmetric parameters α and β. Each of these polynomial systems, as well as their reversed forms θsub.n(x) and θsub.n(x;α,β), has been widely and extensively investigated and applied in the existing literature on the subject. We also briefly consider some recent developments based upon the basic (or quantum or q-) extensions of the Bessel polynomials. Several general families of hypergeometric polynomials, which are actually the truncated or terminating forms of the series representing the generalized hypergeometric function sub.rFsub.s with r symmetric numerator parameters and s symmetric denominator parameters, are also investigated, together with the corresponding basic (or quantum or q-) hypergeometric functions and the basic (or quantum or q-) hypergeometric polynomials associated with sub.rΦsub.s which also involves r symmetric numerator parameters and s symmetric denominator parameters.
Based on 424 firsthand data, this paper provides an in-depth investigation on C??- reduplication in Truku, which varies between first root-consonant (C.sub.1-) and second root-consonant (C.sub.2-) ...copying. The variation has previously been proposed to be either phonologically governed by the presence of glottal stop or semantically governed, dependent upon whether RECIPROCITY is denoted. This paper shows that although both proposals are plausible, they are inconsistent with the data available in previous studies as well as the firsthand data collected for this study. This paper shows instead that the variation of the copying site is both semantically and phonologically governed. Semantically, RECIPROCITY and PLURALITY together behave differently from other semantic functions such as PURPOSE and SIMULTANEOUSLY DOING X. Phonologically, for semantic functions that exhibit variation between C.sub.1??-and C.sub.2??- reduplication, the variation is governed by the phonological features of the initial and the second consonant of the root and are driven by the competition of different forces: the force to prevent marked segments (i.e., ??) and sequences (i.e., ??) in the reduplicant and the force to achieve perfect correspondence between the reduplicant and the base, which are nicely captured by constraint interactions in Optimality Theory. Keywords: Truku; C??- Reduplication; Variable Copying Sites; Firsthand Data; Optimality Theory
