Results 31 to 40 of about 31,890 (192)
On generalized trigonometric functions and series of rational functions
, 2017 Here we introduce a way to construct generalized trigonometric functions associated with any complex polynomials, and the well known trigonometric functions can be seen to associate with polynomial $x^2-1$.
Yu, Han
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Some Trigonometric Polynomials with Extremely Small Uniform Norm
, 2014 An example of trigonometric polynomials with extremely small uniform norm is given. This example demonstrates the potential limits for extension of Sidon's inequality for lacunary polynomials in a certain ...
Grigoriev, Pavel G. +1 more
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A Class of Sheffer Sequences of Some Complex Polynomials and Their Degenerate Types
Mathematics, 2019 We study some properties of Sheffer sequences for some special polynomials with complex Changhee and Daehee polynomials introducing their complex versions of the polynomials and splitting them into real and imaginary parts using trigonometric polynomial ...
Dojin Kim
doaj +1 more source
Orthonormal Systems in Linear Spans
, 2012 We show that any $N$-dimensional linear subspace of $L^2(\mathbb{T})$ admits an orthonormal system such that the $L^2$ norm of the square variation operator $V^2$ is as small as possible. When applied to the span of the trigonometric system, we obtain an
Chevet, Garsia, Marcus, Milman
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q-Ultraspherical polynomials for q a root of unity
, 1996 Properties of the $q$-ultraspherical polynomials for $q$ being a primitive root of unity are derived using a formalism of the $so_q(3)$ algebra.
A. F. Nikiforov +13 more
core +2 more sources
Communications on Pure and Applied Mathematics, EarlyView.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
wiley +1 more source
Mathematics, 2020 We study an energy-dependent potential related to the Rosen–Morse potential. We give in closed-form the expression of a system of eigenfunctions of the Schrödinger operator in terms of a class of functions associated to a family of hypergeometric para ...
Jorge A. Borrego-Morell +2 more
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Connections between Romanovski and other polynomials
, 2007 A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schr\"odinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established.
Weber, H. J.
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New Drain Spacing Formulas Using the Variational Iteration Method
Irrigation and Drainage, EarlyView.ABSTRACT In this study, the drain spacing is computed using the variational iteration method (VIM) to the linearized Boussinesq equation. By applying at most two iterations of the VIM method under three different initial condition scenarios, three equations for drain spacing calculation were derived. These equations predict values of drain spacing that
George Kargas +2 more
wiley +1 more source
AIP Advances, 2018 Chaotic systems are integrated via numerical methods but the main challenge is determining the correct time-step. For instance, traditional numerical methods like Forward Euler (FE) and 4th-order Runge-Kutta (RK), have been applied to simulate and to ...
A. D. Pano-Azucena +3 more
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