Parametric Euler T-sums of odd harmonic numbers

2022/03/26 by Xu, Ce, Yan, Lu
#11A07 #11M32 #11M35 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2203.13996

Abstract

In this paper, we define a parametric variant of generalized Euler sums and call them the (alternating) parametric Euler T-sums. By using the contour integration method and residue theorem, we establish several explicit formulae for the linear parametric Euler T-sums. Furthermore, by applying the results, we obtain explicit formulae for the Hoffman's (alternating) double t-values and Kaneko-Tsumura's (alternating) double T-values.

Related

• Parametric Euler Sums of Harmonic Numbers
• Dirichlet type extensions of Euler sums
• Alternating Euler T-sums and Euler S-sums
• Two Variants of Euler Sums
• Some evaluation of parametric Euler sums