Related papers: Hankel determinants of some polynomial sequences
This paper sets out to introduce the generalized derangement polynomials of order $r $. It then proceeds to establish various identities associated with these polynomials, along with providing recurrence relations for derangement…
We give an explicit evaluation, in terms of products of Jacobsthal numbers, of the Hankel determinants of order a power of two for the period-doubling sequence. We also explicitly give the eigenvalues and eigenvectors of the corresponding…
Using a slightly generalized result of George Andrews and Jet Wimp this note gives a simple computational proof of some Hankel determinants of backwards shifts of convolution powers of Catalan numbers and obtains analogous results for…
The symmetrized Slater determinants of orthogonal polynomials with respect to a non-negative Borel measure are shown to be represented by constant multiple of Hankel determinants of two other families of polynomials, and they can also be…
We investigate the link between rectangular Jack polynomials and Hankel hyperdeterminants. As an application we give an expression of the even power of the Vandermonde in term of Jack polynomials.
Using the language of Riordan arrays, we study a one-parameter family of orthogonal polynomials that we call the restricted Chebyshev-Boubaker polynomials. We characterize these polynomials in terms of the three term recurrences that they…
We compute asymptotics for Hankel determinants and orthogonal polynomials with respect to a discontinuous Gaussian weight, in a critical regime where the discontinuity is close to the edge of the associated equilibrium measure support.…
We study the monic polynomials orthogonal with respect to a symmetric perturbed Gaussian weight $$ w(x;t):=\mathrm{e}^{-x^2}\left(1+t\: x^2\right)^\lambda,\qquad x\in \mathbb{R}, $$ where $t> 0,\;\lambda\in \mathbb{R}$. This weight is…
We consider Hankel determinants of the sequence of Catalan numbers modulo 2 (interpreted as integers 0 and 1) and more generally Hankel determinants where the sum over all permutations reduces to a single signed permutation.
We show that the Hankel determinants of a generalized Catalan sequence satisfy the equations of the elliptic sequence. As a consequence, the coordinates of the multiples of an arbitrary point on the elliptic curve are expressed by the…
We study some polynomials which are related to Hankel determinants of backward shifts of the coefficients of a partial theta function. In this version an appendix is added which gives a simple formula for the coefficients of the reciprocal…
This (partly expository) paper originated from the study of Hankel determinants of convolution powers of Catalan numbers and of Narayana polynomials. This led to some Hankel determinants of signed Catalan numbers whose values are multiples…
In this paper we continue to investigate a certain class of Hankel-like positive definite kernels using their associated orthogonal polynomials. The main result of this paper is about the structure of this kind of kernels.
We calculate the Hankel determinants of sequences of Bernoulli polynomials. This corresponding Hankel matrix comes from statistically estimating the variance in nonparametric regression. Besides its entries' natural and deep connection with…
We introduce a sequence of orthogonal polynomials whose associated moments are the Rayleigh-type sums, involving the zeros of the Bessel derivative $J_\nu'$ of order $\nu$. We also discuss the fundamental properties of those polynomials…
We consider the moment space $\mathcal{M}^{p}_{2n+1}$ of moments up to the order $2n + 1$ of $p_n\times p_n$ real matrix measures defined on the interval $[0,1]$. The asymptotic properties of the Hankel determinant $\{\log\det…
Applying Johann Cigler's Hankel determinant formula in terms of the binomial coefficient determinants, which is simplified from Christian Krattenthale's, we get an explicit formula of Hankel determinants for general. As far as I know, those…
In this paper we investigate algebraic, differential and asymptotic properties of polynomials $p_n(x)$ that are orthogonal with respect to the complex oscillatory weight $w(x)=e^{i\omega x}$ on the interval $[-1,1]$, where $\omega>0$. We…
This note presents some results about Hankel determinants of backwards shifted Catalan-like numbers and related sequences.
E. Heine in the 19th century studied a system of orthogonal polynomials associated with the weight $\left[x(x-\alpha)(x-\beta)\right]^{-\frac{1}{2}}$, $x\in[0,\alpha]$, $0<\alpha<\beta$. A related system was studied by C. J. Rees in 1945,…