相关论文: The Fourier expansion approximation for high-accur…

The expansion of Kummer's hypergeometric function as a series of incomplete Gamma functions is discussed, for real values of the parameters and of the variable. The error performed approximating the Kummer function with a finite sum of…

In this paper, we first establish an evaluation formula to calculate Wiener integrals of functionals on Wiener space. We then apply our evaluation formula to carry out very easily calculating for the analytic Fourier-Feynman transform of…

The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…

Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article,…

A variety of "pseudo-Voigt" functions, i.e. a linear combination of the Lorentz and Gauss function (occasionally augmented with a correction term), have been proposed as a closed-form approximation for the convolution of the Lorentz and…

We obtain series expansion formulas for the Hadamard fractional integral and fractional derivative of a smooth function. When considering finite sums only, an upper bound for the error is given. Numerical simulations show the efficiency of…

In this paper we propose a general strategy for rapidly computing sparse Legendre expansions. The resulting methods yield a new class of fast algorithms capable of approximating a given function $f:[-1,1] \rightarrow \mathbb{R}$ with a…

For compact self-adjoint operators in Hilbert spaces, two algorithms are proposed to provide fully computable a posteriori error estimate for eigenfunction approximation. Both algorithms apply well to the case of tight clusters and multiple…

This paper proposes a novel localized Fourier extension method for approximating non-periodic functions via domain segmentation. By partitioning the computational domain into subregions with uniform discretization scales, the method…

We define an approximate version of the Fourier transform on $2^L$ elements, which is computationally attractive in a certain setting, and which may find application to the problem of factoring integers with a quantum computer as is…

Using geometric considerations, we provide a clear derivation of the integral representation for the error function, known as the Craig formula. We calculate the corresponding power series expansion and prove the convergence. The same…

A new analytical approximation function is proposed to accurately fit the solution of a fractional differential equation of order one-half, whose nonhomogeneous term is defined by a modified Bessel function of the first kind. The exact…

We compute the second moment of the Riemann zeta function for shifted arguments over a domain that extends the ones in the literature. We use the Riemann-Siegel formula for the error term in the approximate functional equation and take the…

Computable and sharp error bounds are derived for asymptotic expansions for linear differential equations having a simple turning point. The expansions involve Airy functions and slowly varying coefficient functions. The sharpness of the…

In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse…

The series expansion at the origin of the Airy function Ai(x) is alternating and hence problematic to evaluate for x > 0 due to cancellation. Based on a method recently proposed by Gawronski, M\"uller, and Reinhard, we exhibit two functions…

An approximate formula for complex Riemann Xi function, previously developed, is used to refine Backlund's estimate of the number of zeros till a chosen imaginary coordinate

In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…

Evaluation of the Voigt function, a convolution of a Lorentzian and a Gaussian profile, is essential in various fields such as spectroscopy, atmospheric science, and astrophysics. Efficient computation of the function is crucial, especially…

In this paper, we consider a method for fast numerical computation of the Fourier transform of a slowly decaying function with given accuracy in given ranges of the frequency. In these decades, some useful formulas for the Fourier transform…