Analytic continuation of the multiple Lucas zeta functions

被引：6

作者：

Meher, Nabin Kumar ^{[1
]}

Rout, Sudhansu Sekhar ^{[2
]}

机构：

[1] Harish Chandra Res Inst HBNI, Chhatnag Rd, Jhunsi 211019, India

[2] Inst Math & Applicat, Bhubaneswar 751029, India

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 468卷 / 02期

关键词：

Analytic continuation; Multiple Lucas zeta function; Lucas sequence; Residues and poles; FIBONACCI NUMBERS; RECIPROCAL SUMS;

D O I：

10.1016/j.jmaa.2018.08.063

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This is a continuation of our previous paper [7], in which multiple Fibonacci zeta functions of depth 2 have been studied. In this article, we consider more general situation. In particular, we prove the meromorphic continuation of the multiple Lucas zeta functions of depth d: Sigma(0 < n1 < ... < nd) 1/U-n1(s1) ... U-nd(sd), where U-n, is the n-th Lucas number of first kind and Sigma(d)(i=j) Re(s(i)) > 0 for 1 <= j <= d. We compute a complete list of poles and their residues. We also prove that the multiple Lucas zeta values at negative integer arguments are rational. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1115 / 1130

页数：16

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