Related papers: Special polynomials and elliptic integrals
The elliptic coordinates are used to build a new families of 2D coordinate systems which are orthogonal and admits the separation of variables. The charts of characteristic curves are constructed for these systems and compared with…
Integrals involving derivatives of Legendre polynomials frequently arise in applications ranging from multipole expansions for processes involving electromagnetic probes to spectral methods in numerical physics. Despite their practical…
We consider regular polynomial interpolation algorithms on recursively defined sets of interpolation points which approximate global solutions of arbitrary well-posed systems of linear partial differential equations. Convergence of the…
We show that various identities from [1] and [3] involving Gould-Hopper polynomials can be deduced from the real but also complex orthogonal invariance of multivariate Gaussian distributions. We also deduce from this principle a useful…
This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and several Analysis-related applications are mentioned.
In this paper we use a set of partial differential equations to prove an expansion theorem for multiple complex Hermite polynomials. This expansion theorem allows us to develop a systematic and completely new approach to the complex Hermite…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
We introduce a canonical form for reduced bases of integral closures of discrete valuation rings, and we describe an algorithm for computing a basis in reduced normal form. This normal form has the same applications as the Hermite normal…
The q-Hermite I-Sobolev type polynomials of higher order are consider for their study. Their hypergeometric representation is provided together with further useful properties such as several structure relations which give rise to a…
The aim of this paper is to study generalized q-analogs of the well-known q-deformed harmonic oscillators and to connect them with q-Hermite polynomials. We give a construction of the appropriate oscillator-like algebras and show that…
The arithmetic of elliptic curves, namely polynomial addition and scalar multiplication, can be described in terms of global sections of line bundles on $E\times E$ and $E$, respectively, with respect to a given projective embedding of $E$…
We use the Legendre polynomials and the Hermite polynomials as two examples to illustrate a simple and systematic technique on deriving asymptotic formulas for orthogonal polynomials via recurrence relations. Another application of this…
We use symbolic expressions for traces of positive integer powers of a Hermitian operator (or, equivalently, coefficients of corresponding characteristic polynomial) to find solutions for the problems as follows: Factorization of…
This paper explores the operational principles and monomiality principle that significantly shape the development of various special polynomial families. We argue that applying the monomiality principle yields novel results while remaining…
We present families of (hyper)elliptic curve which admit an efficient deterministic encoding function.
Techniques for the evaluation of complex polynomials with one and two variables are introduced. Polynomials arise in may areas such as control systems, image and signal processing, coding theory, electrical networks, etc., and their…
In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also…
The aim of this paper is to construct generating functions for new families of special polynomials including the Appel polynomials, the Hermite-Kamp\`e de F\`eriet polynomials, the Milne-Thomson type polynomials, parametric kinds of Apostol…
Generalized trigonometric functions are applied to the Legendre-Jacobi standard form of complete elliptic integrals, and a new form of the generalized complete elliptic integrals of the Borweins is presented. According to the form, it can…
We derive inclusion regions for the eigenvalues of matrix polynomials expressed in a general polynomial basis, which can lead to significantly better results than traditional bounds. We present several applications to engineering problems.