Some Identities with Multi-Generalized q-Hyperharmonic Numbers of Order r

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Chen Z., ÖMÜR N., KOPARAL S., Khan W. A.

Symmetry, vol.15, no.4, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 15 Issue: 4
  • Publication Date: 2023
  • Doi Number: 10.3390/sym15040917
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: multi-generalized q-hyperharmonic numbers of order r, q-analogue of multiple polylogaritms, q-multiple zeta values, q-series
  • Bursa Uludag University Affiliated: Yes


The main purpose of this paper is to define multiple alternative q-harmonic numbers, (Formula presented.) and multi-generalized q-hyperharmonic numbers of order r, (Formula presented.) by using q-multiple zeta star values (q-MZSVs). We obtain some finite sum identities and give some applications of them for certain combinations of q-multiple polylogarithms (Formula presented.) with the help of generating functions. Additionally, one of the applications is the sum involving q-Stirling numbers and q-Bernoulli numbers.