5 papers
Residue Theorem, Regularization and Parity Theorem
Jia Li, Ce Xu
In this paper, we employ contour integration and residue calculus to derive explicit parity formulas for (cyclotomic) multiple zeta values (MZVs). A key innovation lies in applying…
On the Proof of the Genčev-Rucki Conjecture for Multiple Apéry-Like Series
Ce Xu
In this paper, we employ the theories and techniques of hypergeometric functions to provide two distinct proofs of the conjectured identities involving multiple Apéry-like series w…
The Parity of Two Types of Cyclotomic Euler Sums via Contour Integrals
Ce Xu
In this paper, we employ methods of contour integration and residue calculus to investigate the parity of two classes of cyclotomic Euler-type sums. One class involves products of…
Contour Integrations and Parity Results of Cyclotomic Euler -Sums and Multiple -Values
Zhenlu Wang, Ce Xu
We will employ the method of contour integration to investigate the parity results of non-embedded cyclotomic multiple -values, which we refer to as cyclotomic Euler -sums. W…
Contour Integrations and Parity Results of Cyclotomic Euler Sums and Multiple Polylogarithm Function
Hongyuan Rui, Ce Xu
In this paper, we define extended trigonometric functions via series and employ the method of contour integration to investigate the parity of certain cyclotomic Euler sums and mul…