arXiv subjects

Hongyuan Rui

Publications and source records attributed to Hongyuan Rui.

3 recordsLinked to original sources

arXiv2025

Contour Integrations and Parity Results of Hurwitz-type Cyclotomic Euler Sums

In this paper, we investigate the parity of three class of Hurwitz-type cyclotomic Euler sums using the methods of contour integration and residue computation, and derive explicit parity formulas for linear, quadratic, and some higher-order cases. Based on their connection with cyclotomic multiple Hurwitz polylogarithm functions, we further obtain certain parity results for these functions. At the end of the paper, we propose two conjectures regarding the parity and symmetry of multiple Hurwitz polylogarithm functions of arbitrary depth.

math.NT↗

arXiv2025

Contour Integrations and Parity Results of Cyclotomic Euler Sums and Multiple Polylogarithm Function

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 multiple polylogarithm function. We can provide the statement of parity results for cyclotomic Euler sums of arbitrary order, explicit formulas for the parity of cyclotomic linear and quadratic Euler sums, as well as some formulas for the parity of cyclotomic cubic Euler sums and multiple polylogarithms. As a direct corollary, we derive known formulas concerning the parity of classical Euler sums and alternating Euler sums.

math.NT↗

arXiv2023

Berndt-Type Integrals of Order Three and Series Associated with Jacobi Elliptic Functions

In this paper, we first establish explicit evaluations of six classes of hyperbolic sums by special values of the Gamma function by using the tools of the Fourier series expansions and the Maclaurin series expansions of a few Jacobi elliptic functions developed in our previous paper. Then, using the method of contour integrations involving hyperbolic and trigonometric functions, we establish explicit evaluations of two families of Berndt-type integrals of order three by special values of the Gamma function. Furthermore, we present some interesting consequences and illustrative examples.

math.CA↗