Exponential polynomial
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SEVERAL FORMULAS FOR SPECIAL VALUES OF THE BELL POLYNOMIALS OF THE SECOND KIND AND APPLICATIONS Open
In the paper, the authors establish several explicit formulas for special values of the Bell polynomials of the second kind, connect these formulas with the Bessel polynomials, and apply these formulas to give new expressions for the Catal…
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A Note on the Truncated-Exponential Based Apostol-Type Polynomials Open
In this paper, we propose to investigate the truncated-exponential-based Apostol-type polynomials and derive their various properties. In particular, we establish the operational correspondence between this new family of polynomials and th…
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Exponential Convergence of Sum-of-Squares Hierarchies for Trigonometric Polynomials Open
International audience
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Sharp Bernstein-Nikolskii inequalities for polynomials and entire functions of exponential type Open
Точные неравенства Бернштейна -Никольского для полиномов и целых функций экспоненциального типа 1 Д.В. Горбачев (г.Тула) Горбачев Дмитрий Викторович -доктор физико-математических наук, Тульский государственный университет (г
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New inequalities via <i>n</i>-polynomial harmonically exponential type convex functions Open
In this work we introduced a new class of functions called n-polynomial harmonically exponential type convex and study some of their algebraic properties. Several new inequalities via n-polynomial harmonically exponential type convexity ar…
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Generic solutions of equations with iterated exponentials Open
We study solutions of exponential polynomials over the complex field. Assuming Schanuel's Conjecture we prove that certain polynomials of the form
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Generalized quantum exponential function and its applications Open
This article aims to present (q; h)-analogue of exponential function which unifies, extends hand q-exponential functions in a convenient and efficient form. For this purpose, we introduce generalized quantum binomial which serves as an ana…
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Smoothing exponential-polynomial splines for multiexponential decay data Open
In many applications, the definition of fitting models that mimic the behaviour of experimental data is a challenging issue. In this paper a data-driven approach to represent (multi)exponential decay data is presented. We propose a fitting…
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Beyond B-splines: exponential pseudo-splines and subdivision schemes reproducing exponential polynomials Open
The main goal of this paper is to present some generalizations of polynomial B-splines, which include exponential B-splines and the larger family of exponential pseudo-splines. We especially focus on their connections to subdivision scheme…
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Some properties and an application of multivariate exponential polynomials Open
In the paper, the authors introduce a notion “multivariate exponential polynomials” which generalize exponential numbers and polynomials, establish explicit formulas, inversion formulas, and recurrence relations for multivariate exponentia…
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Optimal sampling rates for approximating analytic functions from pointwise samples Open
We consider the problem of approximating an analytic function on a compact interval from its values at $M+1$ distinct points. When the points are equispaced, a recent result (the so-called impossibility theorem) has shown that the best pos…
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On Asymptotic Regimes of Orthogonal Polynomials with Complex Varying Quartic Exponential Weight Open
We study the asymptotics of recurrence coefficients for monic orthogonal polynomials πn(z) with the quartic exponential weight exp[−N(1/2z²+1/4tz⁴)], where t∈C and N∈N, N→∞. Our goal is to describe these asymptotic behaviors globally for t…
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Explicit Formula for Conditional Expectations of Product of Polynomial and Exponential Function of Affine Transform of Extended Cox-Ingersoll-Ross Process Open
In this study, an explicit formula for conditional expectations of the product of polynomial and exponential function of an affine transform is derived under the extended Cox-Ingersoll-Ross (ECIR) process. Moreover, we simplify the result …
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Truncated-Exponential-Based Appell-Type Changhee Polynomials Open
The truncated exponential polynomials em(x) (1), their extensions, and certain newly-introduced polynomials which combine the truncated exponential polynomials with other known polynomials have been investigated and applied in various ways…
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Euler polynomials for the matrix exponential approximation Open
[EN] In this work, a new method to compute the matrix exponential function by using an approximation based on Euler polynomials is proposed. These polynomials are used in combination with the scaling and squaring technique, considering an …
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Montel–Type Theorems for Exponential Polynomials Open
In this paper, we characterize local exponential monomials and polynomials on different types of Abelian groups and we prove Montel-type theorems for these function classes.
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Some inequalities and an application of exponential polynomials Open
In the paper, with the help of the Faà di Bruno formula, properties of the Bell polynomials of the second kind, and the inversion theorem for the Stirling numbers of the first and second kinds, the author presents an explicit formula and a…
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Vieta–Lucas Polynomials for the Brusselator System with the Rabotnov Fractional-Exponential Kernel Fractional Derivative Open
In this study, we provide an efficient simulation to investigate the behavior of the solution to the Brusselator system (a biodynamic system) with the Rabotnov fractional-exponential (RFE) kernel fractional derivative. A system of fraction…
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A Generalized Cubic Exponential B‐Spline Scheme with Shape Control Open
In this paper, a generalized cubic exponential B‐spline scheme is presented, which can generate different kinds of curves, including the conics. Such a scheme is obtained by generalizing the cubic exponential B‐spline scheme based on an it…
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Value distribution of exponential polynomials and their role in the theories of complex differential equations and oscillation theory Open
An exponential polynomial is a finite linear sum of terms P ( z ) e Q ( z ) $P(z)e^{Q(z)}$ , where P ( z ) $P(z)$ and Q ( z ) $Q(z)$ are polynomials. The early results on the value distribution of exponential polynomials can be traced back…
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p-adic estimates of exponential sums oncurves Open
The purpose of this article is to prove a ``Newton over Hodge'' result for exponential sums on curves. Let $X$ be a smooth proper curve over a finite field $\mathbb{F}_q$ of characteristic $p\geq 3$ and let $V \subset X$ be an affine curve…
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New bounds for the exponential function with cotangent Open
In this paper, new bounds for the exponential function with cotangent are found by using the recurrence relation between coefficients in the expansion of power series of the function [Formula: see text] and a new criterion for the monotoni…
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A note on $q$-truncated exponential polynomials Open
In this paper, we introduce the $q$-truncated exponential polynomials by means of the integral form. Certain properties of the $q$-truncated exponential polynomials like series definition, recurrence relations, $q$-differential equations a…
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A Study of the q-Truncated Exponential–Appell Polynomials Open
This article introduces the 2-variable q-truncated exponential–Appell (q-trunc. exp. Appell) polynomials and investigates their fundamental properties. Specific results are derived for the q-trunc. exp. Appell family along with their graph…
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Gauss’s binomial formula and additive property of exponential functions on T(q,h) Open
In this article, we focus our attention on (q,h)-Gauss?s binomial formula from which we discover the additive property of (q; h)-exponential functions. We state the (q,h)-analogue of Gauss?s binomial formula in terms of proper polynomials …
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CONVERGENCE ORDER IN TRAJECTORY ESTIMATION BY PIECEWISE-CUBICS AND EXPONENTIAL PARAMETERIZATION Open
This paper discusses the problem of estimating the trajectory of the unknown curve γ from the sequence of m+1 interpolation points in arbitrary Euclidean space En . The respective knots (in ascending order) are assumed to be unknown. Such …
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EXPONENTIAL POLYNOMIALS AND STRATIFICATION IN THE THEORY OF ANALYTIC INEQUALITIES Open
This paper considers MEP - Mixed Exponential Polynomials as one class of real exponential polynomials. We introduce a method for proving the positivity of MEP inequalities over positive intervals using the Maclaurin series to approximate t…
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Numerical investigation of the fractional diffusion wave equation with exponential kernel via cubic B-Spline approach Open
Splines are piecewise polynomials that are as smooth as they can be without forming a single polynomial. They are linked at specific points known as knots. Splines are useful for a variety of problems in numerical analysis and applied math…
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On the Zeros of Exponential Polynomials Open
We consider the problem of deciding the existence of real roots of real-valued exponential polynomials with algebraic coefficients. Such functions arise as solutions of linear differential equations with real algebraic coefficients. We foc…
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Application of the AAK theory for sparse approximation of exponential sums Open
In this paper, we derive a new method for optimal $\ell^{1}$- and $\ell^2$-approximation of discrete signals on ${\mathbb N}_{0}$ whose entries can be represented as an exponential sum of finite length. Our approach employs Prony's method …