{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,27]],"date-time":"2026-05-27T21:33:21Z","timestamp":1779917601081,"version":"3.53.1"},"reference-count":35,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2023,4,14]],"date-time":"2023-04-14T00:00:00Z","timestamp":1681430400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["62272112"],"award-info":[{"award-number":["62272112"]}]},{"name":"National Natural Science Foundation of China","award":["2023A1515011998"],"award-info":[{"award-number":["2023A1515011998"]}]},{"name":"Natural Science Foundation of Guangdong Province of China","award":["62272112"],"award-info":[{"award-number":["62272112"]}]},{"name":"Natural Science Foundation of Guangdong Province of China","award":["2023A1515011998"],"award-info":[{"award-number":["2023A1515011998"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main purpose of this paper is to define multiple alternative q-harmonic numbers, Hnk;q and multi-generalized q-hyperharmonic numbers of order r, Hnrk;q 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 Liq;k1,k2,\u2026,kdt1,t2,\u2026,td with the help of generating functions. Additionally, one of the applications is the sum involving q-Stirling numbers and q-Bernoulli numbers.<\/jats:p>","DOI":"10.3390\/sym15040917","type":"journal-article","created":{"date-parts":[[2023,4,14]],"date-time":"2023-04-14T10:29:16Z","timestamp":1681468156000},"page":"917","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Some Identities with Multi-Generalized q-Hyperharmonic Numbers of Order r"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8039-2141","authenticated-orcid":false,"given":"Zhihua","family":"Chen","sequence":"first","affiliation":[{"name":"Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ne\u015fe","family":"\u00d6m\u00fcr","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Kocaeli University, Kocaeli 41380, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9574-9652","authenticated-orcid":false,"given":"Sibel","family":"Koparal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Bursa Uluda\u011f University, Bursa 16059, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4681-9885","authenticated-orcid":false,"given":"Waseem Ahmad","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Natural Sciences, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al Khobar 31952, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,4,14]]},"reference":[{"key":"ref_1","first-page":"140","article-title":"Meditationes circa singulare serierum genus","volume":"20","author":"Euler","year":"1776","journal-title":"Novi Comm. Acad. Sci. Petropol."},{"key":"ref_2","first-page":"210","article-title":"Values of zeta-functions and their applications","volume":"Volume II","author":"Zagier","year":"1994","journal-title":"First European Congress of Mathematics"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"275","DOI":"10.2140\/pjm.1992.152.275","article-title":"Multiple harmonic numbers","volume":"152","author":"Hoffman","year":"1992","journal-title":"Pac. J. 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