Related papers: Chandrasekhar polynomials -- A brief review
We provide a simple method to recognize classical orthogonal polynomials on lattices defined only by their coefficients of the three term recurrence relation.
We give a short introduction to the theory of twisted Alexander polynomials of a 3--manifold associated to a representation of its fundamental group. We summarize their formal properties and we explain their relationship to twisted…
The Christoffel-Darboux kernels for orthogonal polynomials in several real variables are investigated within the context of the three term recurrence relation reformulated for this purpose. Examples of orthogonal polynomials on the unit…
This is a review of ($q$-)hypergeometric orthogonal polynomials and their relation to representation theory of quantum groups, to matrix models, to integrable theory, and to knot theory. We discuss both continuous and discrete orthogonal…
We describe various aspects of the Al-Salam-Carlitz $q$-Charlier polynomials. These include combinatorial descriptions of the moments, the orthogonality relation, and the linearization coefficients.
We give a survey of the analytic theory of matrix orthogonal polynomials.
In this short review, I'll discuss the background, applicability and prospects of collinear factorization in quantum chromodynamics.
In this paper, with the help of trinomial coefficients we study some arithmetic properties of certain determiants involving reciprocals of binary quadratic forms over finite fields.
We consider polynomials that are defined as Wronskians of certain sets of Hermite polynomials. Our main result is a recurrence relation for these polynomials in terms of those of one or two degrees smaller, which generalizes the well-known…
We consider optical tomography with structured illumination in spatial-frequency domain using the three-dimensional radiative transport equation. Without the diffusion approximation, the radiative transport equation is solved by the…
New bispectral polynomials orthogonal on a quadratic bi-lattice are obtained from a truncation of Wilson polynomials. Recurrence relation and difference equation are provided. The recurrence coefficients can be encoded in a perturbed…
Motion polynomials are a specific type of polynomial over a Clifford algebra that can conveniently describe rational motions. There exists an algorithm for the factorization of motion polynomials that works in generic cases. It hinges on…
We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…
Cyclotomic polynomials play an important role in several areas of mathematics and their study has a very long history, which goes back at least to Gauss (1801). In particular, the properties of their coefficients have been intensively…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
The spread between two lines in rational trigonometry replaces the concept of angle, allowing the complete specification of many geometrical and dynamical situations which have traditionally been viewed approximately. This paper…
We analyze and partially solve system of recurrences that can be derived from the properties of martingale orthogonal polynomials that characterize quadratic harnesses (QH). We also specify conditions for the existence of moments of one…
A combinatorial theory for type $R_I$ orthogonal polynomials is given. The ingredients include weighted generalized Motzkin paths, moments, continued fractions, determinants, and histories. Several explicit examples in the Askey scheme are…
A sequence of coefficients appearing in a recurrence for the Narayana polynomials is generalized. The coefficients are given a probabilistic interpretation in terms of beta distributed random variables. The recurrence established by M.…
We formulate and prove a general recurrence relation that applies to integrals involving orthogonal polynomials and similar functions. A special case are connection coefficients between two sets of orthonormal polynomials, another example…