Related papers: Refinement of the theory and convergence of the Si…
Based on the Sinc approximation combined with the tanh transformation, Haber derived an approximation formula for numerical indefinite integration over the finite interval (-1, 1). The formula uses a special function for the basis…
The Sinc approximation is known to be a highly efficient approximation formula for rapidly decreasing functions. For unilateral rapidly decreasing functions, which rapidly decrease as $x\to\infty$ but does not as $x\to-\infty$, an…
F. Stenger proposed efficient approximation formulas for derivatives over infinite intervals. These formulas were derived by combining the Sinc approximation with appropriate conformal maps. It has been demonstrated that these formulas can…
The Sinc approximation is a function approximation formula that attains exponential convergence for rapidly decaying functions defined on the whole real axis. Even for other functions, the Sinc approximation works accurately when combined…
The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier integral. The double exponential transformation is not only useful for numerical computations but it is…
A Sinc-collocation method has been proposed by Stenger, and he also gave theoretical analysis of the method in the case of a `scalar' equation. This paper extends the theoretical results to the case of a `system' of equations. Furthermore,…
The Sinc quadrature and the Sinc indefinite integration are approximation formulas for definite integration and indefinite integration, respectively, which can be applied on any interval by using an appropriate variable transformation.…
The double-exponential Sinc-collocation method is known as a super-accurate method for solving initial value problems of ordinary differential equations, for which the error decreases almost exponentially as a function of the number of…
The Sinc approximation has shown high efficiency for numerical methods in many fields. Conformal maps play an important role in the success, i.e., appropriate conformal map must be employed to elicit high performance of the Sinc…
Two different Sinc-collocation methods for Volterra integral equations of the second kind have been independently proposed by Stenger and Rashidinia--Zarebnia. However, their relation remains unexplored. This study theoretically examines…
Circular Synthetic aperture sonars (CSAS) capture multiple observations of a scene to reconstruct high-resolution images. We can characterize resolution by modeling CSAS imaging as the convolution between a scene's underlying point…
Convergence theory is an extension of general topology. In contrast with topology, it is closed under some important operations, like exponentiation. With all its advantages, convergence theory remains rather unknown. It is an aim of this…
We propose a method based on sinc series approximations for computing the Rayleigh-Sommerfeld and Fresnel diffraction integrals of optics. The diffraction integrals are given in terms of a convolution, and our proposed numerical approach is…
Inversion of function sinc(x) is studied. New series and integral representations of branches of inverse function are obtained using Fourier analysis.
The convolution quadrature theory is a systematic approach to analyse the approximation of the Riemann-Liouville fractional operator $I^{\alpha}$ at node $x_{n}$. In this paper, we develop the shifted convolution quadrature ($SCQ$) theory…
A method of numerically evaluating slowly convergent monotone series is described. First, we apply a condensation transformation due to Van Wijngaarden to the original series. This transforms the original monotone series into an alternating…
By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.
In \cite{CGPWW2021}, it was conjectured that a particular shifted sum of even divisor sums vanishes, and in \cite{SDK}, a formal argument was given for this vanishing. Shifted convolution sums of this form appear when computing the Fourier…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
In this paper, we study the entanglement entropy in string theory in the simplest setup of dividing the nine dimensional space into two halves. This corresponds to the leading quantum correction to the horizon entropy in string theory on…