Analytic continuation of the multiple Lucas zeta functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:468

Article

Meher, Nabin Kumar¹  Rout, Sudhansu Sekhar² 

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

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

关键词: Analytic continuation;    Multiple Lucas zeta function;    Lucas sequence;    Residues and poles;   

DOI  :  10.1016/j.jmaa.2018.08.063

来源: Elsevier

【 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.

【 授权许可】

Free