5 papers · 1 filter
Alternating Multiple Mixed Values: Regularization, Special Values, Parity and Dimension Conjectures
Ce Xu, Lu Yan, Jianqiang Zhao
In this paper, we define and study a variant of multiple zeta values (MZVs) of level four, called alternating multiple mixed values or alternating multiple -values (AMMVs), form…
Apéry-Like Sums and Colored Multiple Zeta Values
Ce Xu, Jianqiang Zhao
In this article we shall survey some recent progress on the study of Apéry-like sums which are multiple variable generalizations of the two sums Apéry used in his famous proof of…
Parametric Apéry-type Series and Hurwitz-type Multiple Zeta Values
Masanobu Kaneko, Weiping Wang, Ce Xu +1
In this paper, we extend the main results of a 2024 \emph{Advances in Applied Mathematics} paper \cite{XuZhao2021c} about Apéry-type series involving central binomial coefficients…
Reciprocal Hyperbolic Series of Ramanujan Type
Ce Xu, Jianqiang Zhao
This paper presents an approach to summing a few families of infinite series involving hyperbolic functions, some of which were first studied by Ramanujan. The key idea is based on…
Berndt-Type Integrals and Series Associated with Ramanujan and Jacobi Elliptic Functions
Ce Xu, Jianqiang Zhao
In this paper, we evaluate in closed forms two families of infinite integrals containing hyperbolic and trigonometric functions in their integrands. We call them Berndt-type integr…