Zobrazeno 1 - 10
of 1 130
pro vyhledávání: '"Glasser M"'
Publikováno v:
SIGMA 20 (2024), 079, 14 pages
Through the application of an evaluation technique based on cyclotomic multiple zeta values recently due to Au, we solve open problems on inverse binomial series that were included in a 2010 analysis textbook by Chen.
Comment: a sequel to arXiv:
Comment: a sequel to arXiv:
Externí odkaz:
http://arxiv.org/abs/2403.16945
We introduce and prove evaluations for families of multiple elliptic integrals by solving special types of ordinary and partial differential equations. As an application, we obtain new expressions of Ramanujan-type series of level 4 and associated si
Externí odkaz:
http://arxiv.org/abs/2403.07298
Autor:
Glasser, M. L.
An $n$-dimensional generalization of the Onsager Ising partition function integral is reduced to a single integral and applied to evaluate the partition function and residual entropy of an eight vertex model.
Comment: 4 pages
Comment: 4 pages
Externí odkaz:
http://arxiv.org/abs/2307.06854
Autor:
Glasser, M. L.
This short note investigates a number of index integrals of products of the Lommel functions $s_{\mu,\nu}(a)$ and uncovers an integral relationship. between this function and the Tchebyshev polynomials $T_{2n}(x)$.
Comment: 5 Pages
Comment: 5 Pages
Externí odkaz:
http://arxiv.org/abs/2203.03395
Autor:
Glasser, M. L.
It is proposed that the validity, or not, of the Riemann Hypothesis might be established on the basis of the integral $$\int\frac{\xi(2s)}{\xi(s)}ds$$ where $$\xi(s)=(s-1)\pi^{-s/2}\Gamma(1+s/2)\zeta(s).$$
Comment: 3pages
Comment: 3pages
Externí odkaz:
http://arxiv.org/abs/2108.06860
In this work we analyze the statistical thermodynamics of Diced lattice carriers employing a Greens function formulation to examine the grand potential, Helmholtz free energy, the grand and ordinary partition functions and entropy. This facilitates t
Externí odkaz:
http://arxiv.org/abs/2008.05113
Autor:
Glasser, M. L.
In this note a one-dimensional band model is proposed based on a periodic Dirac comb having an identical mass distribution $m(x)$ . in each unit cell. The mass function is represented as a Hermitian, non-local separable operator. Two specific cases--
Externí odkaz:
http://arxiv.org/abs/1910.00549
Autor:
Glasser, M. L.
This note investigates a number of integrals of and integral equations satisfied by Riemann's $\xi-$function. A different, less restrictive, derivation of one of his key identities is provided. This work centers on the critical strip and it is argued
Externí odkaz:
http://arxiv.org/abs/1901.07011
Publikováno v:
Journal of Integer Sequences 22 (2019), article 19.4.7, 16 pp
Let $f_0(z) = \exp(z/(1-z))$, $f_1(z) = \exp(1/(1-z))E_1(1/(1-z))$, where $E_1(x) = \int_x^\infty e^{-t}t^{-1}{\,d}t$. Let $a_n = [z^n]f_0(z)$ and $b_n = [z^n]f_1(z)$ be the corresponding Maclaurin series coefficients. We show that $a_n$ and $b_n$ ma
Externí odkaz:
http://arxiv.org/abs/1812.00316
Autor:
Glasser, M. L.
The Moll-Arias de Reyna integral [1] $$\int_0^{\infty}\frac{dx}{(x^2+1)^{3/2}}\frac{1}{\sqrt{\varphi(x)+\sqrt{\varphi(x)}}}$$ $$\varphi(x)=1+\frac{4}{3}\left(\frac{x}{x^2+1}\right)^2$$ is generalised and several values are given.
Comment: 4 page
Comment: 4 page
Externí odkaz:
http://arxiv.org/abs/1802.10564