Results 1 to 10 of about 590,010 (44)

A Few Finite Trigonometric Sums [PDF]

Mathematics 5, 13 (2017), 2016
Finite trigonometric sums occur in various branches of physics, mathematics, and their applications. These sums may contain various powers of one or more trigonometric functions. Sums with one trigonometric function are known, however sums with products of trigonometric functions can get complicated and may not have a simple expressions in a number of ...
Agrawal, Pankaj, Datta, Chandan
arxiv   +4 more sources

A note on trigonometric approximations of Bessel functions of the first kind and trigonometric power sums [PDF]

Fundamental Journal of Mathematics and Applications 5 (4) (2022) 266-272, 2022
I reconsider the approximation of Bessel functions with finite sums of trigonometric functions, in the light of recent evaluations of Neumann-Bessel series with trigonometric coefficients. A proper choice of the angle allows for an efficient choice of the trigonometric sum.
arxiv   +1 more source

Properties of generalized univariate hypergeometric functions [PDF]

, 2006
Based on Spiridonov's analysis of elliptic generalizations of the Gauss hypergeometric function, we develop a common framework for 7-parameter families of generalized elliptic, hyperbolic and trigonometric univariate hypergeometric functions.
B. Nassrallah, D.P. Gupta, E. Koelink, E. Koelink, E. Koelink, E. M. Rains, F. J. van de Bult, F.J. Bult van de, G. Gasper, G. Letzter, J. V. Stokman, J.F. Diejen van, J.V. Stokman, J.V. Stokman, M. Noumi, M. Put van der, M. Rahman, M.E.H. Ismail, S. Lievens, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, S.N.M. Ruijsenaars, T. Shintani, V.P. Spiridonov, V.P. Spiridonov, W. Groenevelt, Y. Komori   +27 more
core   +4 more sources

k-Fractional trigonometric functions [PDF]

, 2014
Based on the k-Mittag-Lefler function and the k-α-Exponential Function we introduce families of functions that allows us define new fractional trigonometric functions that contain the classical trigonometric functions as particular case for some ...
Cerutti, Ruben Alejandro, Luque, Luciano Leonardo   +1 more
core   +1 more source

Elliptic and K-theoretic stable envelopes and Newton polytopes [PDF]

, 2018
In this paper we consider the cotangent bundles of partial flag varieties. We construct the $K$-theoretic stable envelopes for them and also define a version of the elliptic stable envelopes. We expect that our elliptic stable envelopes coincide with the
Rimányi, R., Tarasov, V., Varchenko, A.
core   +3 more sources

Extended trigonometric Cherednik algebras and nonstationary Schr\"odinger equations with delta-potentials [PDF]

, 2012
We realize an extended version of the trigonometric Cherednik algebra as affine Dunkl operators involving Heaviside functions. We use the quadratic Casimir element of the extended trigonometric Cherednik algebra to define an explicit nonstationary Schr ...
Gaudin M., Heckman G. J., J. T. Hartwig, J. V. Stokman, Opdam E. M.   +4 more
core   +2 more sources

Approximation, regularization and smoothing of trigonometric splines [PDF]

arXiv, 2021
The methods of approximation, regularization and smoothing of trigonometric interpolation splines are considered in the paper. It is shown that trigonometric splines can be considered from two points of view - as a trigonometric Fourier series and as discrete trigonometric Fourier series according to certain systems of functions that are smoothness ...
arxiv  

Lasso trigonometric polynomial approximation for periodic function recovery in equidistant points [PDF]

arXiv, 2022
In this paper, we propose a fully discrete soft thresholding trigonometric polynomial approximation on $[-\pi,\pi],$ named Lasso trigonometric interpolation. This approximation is an $\ell_1$-regularized discrete least squares approximation under the same conditions of classical trigonometric interpolation on an equidistant grid.
arxiv  

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
core   +1 more source

Extended Levett trigonometric series [PDF]

arXiv, 2023
An extension of two finite trigonometric series is studied to derive closed form formulae involving the Hurwitz-Lerch zeta function. The trigonometric series involves angles with a geometric series involving the powers of 3. These closed formulae are used to derive composite finite series involving special functions, trigonometric functions and ...
arxiv