相关论文: New series representation for Madelung constant
Lattice sums of cuboidal lattices, which connect the face-centered with the mean-centered and the body-centered cubic lattices through parameter dependent lattice vectors, are evaluated by decomposing them into two separate lattice sums…
In an unbounded plane, straight lines are used extensively for mathematical analysis. They are tools of convenience. However, those with high slope values become unbounded at a faster rate than the independent variable. So, straight lines,…
Using a clear and straightforward approach, we discover and prove new binary digit extraction BBP-type formulas for polylogarithm constants. Some known results are also rediscovered in a more direct and elegant manner. Numerous…
In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account.…
We study convergence of 3D lattice sums via expanding spheres. It is well-known that, in contrast to summation via expanding cubes, the expanding spheres method may lead to formally divergent series (this will be so e.g. for the classical…
By using Beta Dirichlet series and then Eisenstein series we ca represent primes with first a good approximation and an exact expression. This can be done with arbitrary prime (up to 10^101).
By integrating a series provided by Knopp, a series representation of the Euler-Mascheroni constant arises. The infinite sum representation of {\gamma} is determined through Fourier series (sawtooth wave).
The author derives new family of series representations for the values of the Riemann Zeta function $\zeta(s)$ at positive odd integers. For $n\in\mathbb{N}$, each of these series representing $\zeta(2n+1)$ converges remarkably rapidly with…
We supplement a very recent paper of R. Crandall concerned with the multiprecision computation of several important special functions and numbers. We show an alternative series representation for the Riemann and Hurwitz zeta functions…
This communication shows the track for finding a solution for a sin(kx)/k**2 series and a fresh representation for the Euler's Gamma function in terms of Riemann's Zeta function. We have found a new series expression for the logarithm as a…
Finding a computationally efficient algorithm for the inverse continuous wavelet transform is a fundamental topic in applications. In this paper, we show the convergence of the inverse wavelet transform.
In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…
A new representation for a regular solution of the radial Dirac system of a special form is obtained. The solution is represented as a Neumann series of Bessel functions uniformly convergent with respect to the spectral parameter. For the…
Determination of linear combination of exponential functions with unknown rate constants from its sampled values is a problem of considerable interest. Here we present a constructive and explicit solution to this problem. Moments of such…
Recently, Sun [preprint, arXiv: 2210.07238v7] proposed two conjectural series for the mathematical constant $\zeta(4)$ and two conjectural series for the mathematical constant $\zeta(5)$. In terms of the operator method and two…
We derive a new integral formula for the Stieltjes constants. The new formula permits easy computations as well as an exact approximate asymptotic formula. Both the sign oscillations and the leading order of growth are provided. The formula…
We consider the series of reciprocals of those positive integers with exactly $k$ occurrences of a given $b$-ary digit $d$ (Irwin series), and obtain geometrically convergent representations for their sums. They are expressed in terms of…
This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function…
We present a variety of series representations of the Stieltjes and related constants, the Stieltjes constants being the coefficients of the Laurent expansion of the Hurwitz zeta function zeta(s,a) about s=1. Additionally we obtain series…
This paper is concerned with the study of the fractional finite sums theory. We present the classes of functions for which it is possible to characterize the constant related to the derivative of fractional sums (denominated by essence of a…