由半双曲线安全分布获得的卡塔兰常数、阿佩里常数和欧拉数的新表示
数论
2025-02-11 v1
摘要
presented of new expressions and bounds for Catalan's and Apery's constants, derived from the half hyperbolic secant distribution. These constants are obtained by using expressions for the Lorenz curve, the Gini and Theil indices, convolutions and a mixture of distributions, among other approaches. The new expressions are presented both in terms of integral (simple and double) representation and also as an interesting series representation. Some of these features are well known, while others are new. In addition, some integral representations of Euler's numbers are obtained.
引用
@article{arxiv.2502.06340,
title = {New Representations of Catalan's Constant, Apery's Constant and the Euler Numbers Obtained from the Half Hyperbolic Secant Distribution},
author = {Emilio Gómez-Déniz and José María Sarabia},
journal= {arXiv preprint arXiv:2502.06340},
year = {2025}
}
备注
21 pages