{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:44:33Z","timestamp":1760233473492,"version":"build-2065373602"},"reference-count":14,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2021,1,7]],"date-time":"2021-01-07T00:00:00Z","timestamp":1609977600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002468","name":"Dong-A university","doi-asserted-by":"publisher","award":["Dong-A university"],"award-info":[{"award-number":["Dong-A university"]}],"id":[{"id":"10.13039\/501100002468","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The main aim of this article is to investigate some interesting symmetric identities for the Dirichlet-type multiple (p,q)-L function. We use this function to examine the symmetry of the generalized higher-order (p,q)-Euler polynomials related to \u03c7. First, the generalized higher-order (p,q)-Euler numbers and polynomials related to \u03c7 are defined. We also give a few new symmetric properties for the Dirichlet-type multiple (p,q)-L-function and generalized higher-order (p,q)-Euler polynomials related to \u03c7.<\/jats:p>","DOI":"10.3390\/sym13010095","type":"journal-article","created":{"date-parts":[[2021,1,10]],"date-time":"2021-01-10T23:03:42Z","timestamp":1610319822000},"page":"95","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Symmetric Properties for Dirichlet-Type Multiple (p,q)-L-Function"],"prefix":"10.3390","volume":"13","author":[{"given":"Kyung-Won","family":"Hwang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Dong-A University, Busan 49315, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ravi P.","family":"Agarwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas A&amp;M University-Kingsville, Kingsville, TX 78363, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cheon-Seoung","family":"Ryoo","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Hannam University, Daejeon 34430, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,7]]},"reference":[{"key":"ref_1","first-page":"374","article-title":"On the theory of the multiple Gamma functions","volume":"19","author":"Barnes","year":"1904","journal-title":"Trans. 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Inform."},{"key":"ref_10","unstructured":"Abramowitz, M., and Stegun, I.A. (1972). Handbook of Mathematical Functions, Dover Publications."},{"key":"ref_11","first-page":"457","article-title":"Some symmetry identities for the Euler polynomials","volume":"30","author":"Yang","year":"2010","journal-title":"J. Math. Res. Expos."},{"key":"ref_12","first-page":"390","article-title":"Some generalizations and basic (or q-) extensions of the Bernoulli, Euler and Genocchi polynomials","volume":"5","author":"Srivastava","year":"2011","journal-title":"Appl. Math. Inform. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"557","DOI":"10.3906\/mat-1703-114","article-title":"Construction of some new families of Apostal-type numbers and polynomials via Dirichlet character and p-adic q-integrals","volume":"42","author":"Simsek","year":"2018","journal-title":"Turk. J. Math."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Andrews, G.E., Askey, R., and Roy, R. (1999). Special Functions. Encyclopedia of Mathematics and Its Applications, Cambridge University Press.","DOI":"10.1017\/CBO9781107325937"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/95\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:08:09Z","timestamp":1760159289000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/13\/1\/95"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,7]]},"references-count":14,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["sym13010095"],"URL":"https:\/\/doi.org\/10.3390\/sym13010095","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2021,1,7]]}}}