The multiplicate form of Gould–Hsu’s inverse series relations enables to investigate the dual relations of the Chu–Vandermonde–Gauß’s, the Pfaff–Saalschütz’s summation theorems and the binomial convolution formula due to Hagen and Rothe. Several identitity and reciprocal relations are thus established for terminating hypergeometric series. By virtue of the duplicate inversions, we establish sev...

We show that an arbitrary Hankel matrix of a nite rank admits a Vandermonde decomposition: H = V T DV , where V is a con-uent Vandermonde matrix and D is a block diagonal matrix. This result was rst derived by Vandevoorde; our contribution here is a presentation that uses only linear algebra, speciically, the Jordan canonical form. We discuss the choices for computing this decomposition in only...

In this paper, we review some potential applications of random Vandermonde matrices in the field of signal processing and wireless communications. Using asymptotic results based on the theory of random Vandermonde matrices, we show through several application examples, namely deconvolution, wireless capacity analysis and sampling theory, the research potential of this theory. Quite surprisingly...

Motivated by the famous Skolem-Mahler-Lech theorem we initiate in this paper the study of a natural class of determinantal varieties, which we call Vandermonde varieties. They are closely related to the varieties consisting of all linear recurrence relations of a given order possessing a non-trivial solution vanishing at a given set of integers. In the regular case, i.e., when the dimension of ...

Pλ(y; θ), (1) where δ := (n− 1, n− 2, . . . , 1, 0) and λ are partitions, aδ = ∏ 1≤i<j≤n(yi − yj) is the Vandermonde determinant and u is a free parameter. Under a general result, S. Sahi proves [8, Theorem 5.2] the existence of a unique polynomial P ∗ μ(y; θ), now known as shifted Jack polynomials, satisfying a certain vanishing condition. In the special case θ = 1, Okounkov and Olshanski [6,7...

This study was undertaken to examine the cell cycle characteristics of bovine fetal and adult somatic cells (fetal fibroblasts, adult skin and muscle cells, and cumulus cells) after culture under a variety of conditions; 1) growth to 60-70% confluency (cycling), 2) serum starvation, 3) culture to confluency. Cell -cycle phases were determined by flow cytometry with propidium iodide staining ena...