多个多对数的双参数变形和

Pub Date : 2021-10-08 DOI:10.1007/s11040-021-09407-0

Masaki Kato

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引用次数: 1

摘要

本文引入了一个多对数双参数变形和的生成函数Φ2(a;p,q)，并研究了它所满足的q差分方程。我们证明了将Φ2(a;p,q)展开为参数p的幂级数，然后用变分常数的方法可以求解这个q-差分方程。通过将\(p \rightarrow 0\)代入主要定理，我们发现q插值的多个zeta值的和的生成函数可以用q超几何函数3ϕ2表示，这是由Li-Wakabayashi提出的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Sums of Two-Parameter Deformations of Multiple Polylogarithms

In this paper, we introduce a generating function of sums of two-parameter deformations of multiple polylogarithms, denoted by Φ₂(a;p,q), and study a q-difference equation satisfied by it. We show that this q-difference equation can be solved by expanding Φ₂(a;p,q) into power series of the parameter p and then using the method of variation of constants. By letting \(p \rightarrow 0\) in the main theorem, we find that the generating function of sums of q-interpolated multiple zeta values can be written in terms of the q-hypergeometric function ₃ϕ₂, which is due to Li-Wakabayashi.

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