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On alternating sum formulas for the Arakawa-Kaneko multiple zeta values

Yuta Nishimura

Abstract

In this paper, we construct generating functions of alternating sums for the Arakawa-Kaneko zeta values. From the expressions, we show alternating sum formulas for them. Based on these results, we apply the same method to other zeta values.

On alternating sum formulas for the Arakawa-Kaneko multiple zeta values

Abstract

In this paper, we construct generating functions of alternating sums for the Arakawa-Kaneko zeta values. From the expressions, we show alternating sum formulas for them. Based on these results, we apply the same method to other zeta values.
Paper Structure (4 sections, 17 theorems, 44 equations)

This paper contains 4 sections, 17 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. Alternating sum for the Arakawa-Kaneko multiple zeta values
  3. Alternating sums for the interpolated multiple zeta values
  4. Alternating sum for a certain t-Arakawa-Kaneko multiple zeta values

Key Result

Theorem 2.1

For $k_1,\ldots, k_r\geq1$ and $m\geq1$, we have

Theorems & Definitions (37)

  • Theorem 2.1: KO
  • Proposition 2.2
  • proof
  • Definition 2.3
  • Lemma 2.4
  • Proposition 2.5: CE
  • Theorem 2.6
  • proof
  • Definition 3.1: Y1
  • Remark 1
  • ...and 27 more