Related papers: Curvilinearity and Orthogonality
In this paper, we first construct generalized $q^2$-cosine, $q^2$-sine and $q^2$-exponential functions. We then use $q^2$-exponential function in order to define and investigate a $q^2$-Fourier transform. We establish $q$-analogues of…
In this chapter are given necessary and sufficient conditions for the regularity of solutions of the functional equation appearing in the theory of classical orthogonal polynomials. In addition, we also present the functional Rodrigues…
In this paper, we describe s-logarithmically convex functions in the first and second sense which are connected with the ordinary logatihmic convex and s-convex in the first and second sense. Afterwards, some new inequalities related to…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
The parabolic functions are introduced in analogy to the circular and hyperbolic cases. We discuss the relevant properties, the geometrical interpretation and touch on possible generalizations and their link with the modular elliptic…
A unified algebraic interpretation of both finite families of orthogonal polynomials and biorthogonal rational functions of $q$-Hahn type is provided. The approach relies on the meta $q$-Hahn algebra and its finite-dimensional bidiagonal…
A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…
This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given.…
In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.
The aim of the work is to construct new polynomial systems, which are solutions to certain functional equations which generalize the second-order differential equations satisfied by the so called classical orthogonal polynomial families of…
Orthogonal arrays are arguably one of the most fascinating and important statistical tools for efficient data collection. They have a simple, natural definition, desirable properties when used as fractional factorials, and a rich and…
We study seminormalization of affine complex varieties. We show that polynomials on the seminormalization correspond to the rational functions which are continuous for the Euclidean topology. We further study this type of functions which…
Let a sequence $(P_n)$ of polynomials in one complex variable satisfy a recurre ce relation with length growing slowlier than linearly. It is shown that $(P_n) $ is an orthonormal basis in $L^2_{\mu}$ for some measure $\mu$ on $\C$, if and…
Finite families of biorthogonal rational functions and orthogonal polynomials of Racah-type are studied within a unified algebraic framework based on the meta Racah algebra and its finite-dimensional representations. These functions are…
We continue previous work to count non-equivalent dynamical systems over finite fields generated by polynomials or rational functions.
This report (written in French) is devoted to studying special functions the most used in physics. Special functions are a very broad branch of mathematics, theoretical physics, and mathematical physics. They appeared in the nineteenth…
We consider orthogonal polynomials on the unit circle associated with certain semi-classical weight functions. This means that the Pearson-type differential equations satisfied by these weight functions involve two polynomials of degree at…
We explore a class of meromorphic functions on elliptic curves, termed \emph{elliptic orthogonal a-polynomials} ($a$-EOPs), which extend the classical notion of orthogonal polynomials to compact Riemann surfaces of genus one. Building on…
We prove that the Nevalinna-Pick algorithm provides different homeomorphisms between certain topological spaces of measures, analytic functions and sequences of complex numbers. This algorithm also yields a continued fraction expansion of…