We consider finite sequences s ∈ D n where D is a commutative, unital, integral domain. We prove three sets of identities (possibly with repetitions), each involving 2n polynomials associated to s. The right-hand side of these identities is a recursively-defined (non-zero) 'product-of-discrepancies'. There are implied iterative algorithms (of quadratic complexity) for the left-hand side coeffic...

We study integer sequences and transforms that operate on them. Many of these transforms are defined by triangular arrays of integers, with a particular focus on Riordan arrays and Pascal-like arrays. In order to explore the structure of these transforms, use is made of methods coming from the theory of continued fractions, hypergeometric functions, orthogonal polynomials and most importantly f...

This paper details a comparative analysis on time taken by the present and proposed methods to compute the Zernike moments, Zpq. The present method comprises of Direct, Belkasim’s, Prata’s, Kintner’s and Coe3cient methods. We propose a new technique, denoted as q-recursive method, speci5cally for fast computation of Zernike moments. It uses radial polynomials of 5xed order p with a varying inde...

In the paper, the authors view some ordinary differential equations and their solutions from the angle of (the generalized) derivative polynomials and simplify some known identities for the Bernoulli numbers and polynomials, the Frobenius-Euler polynomials, the Euler numbers and polynomials, in terms of the Stirling numbers of the first and second kinds.

Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspher...

formulae expressing explicitly the coefficients of an expansion of double jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. extension to expansion of triple jacobi polynomials is given. the results for the special cases of double and triple ultraspher...

In this paper, we study factorizations in the additive monoids of positive algebraic valuations N0[α] semiring polynomials N0[X] using a methodology introduced by D. Anderson, F. and M. Zafrullah 1990. A cancellative commutative monoid is atomic if every non-invertible element factors into irreducibles. We begin determining when atomic, give an explicit description its set An finite factorizati...

Inferences we make about underlying cognitive processes can be jeopardized in two ways due to problematic forms of aggregation. First, averaging across individuals is typically considered a very useful tool for removing random variability. The threat is that averaging across subjects leads to averaging across different cognitive strategies, thus harming our inferences. The second threat comes f...