{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:41:58Z","timestamp":1740134518993,"version":"3.37.3"},"reference-count":21,"publisher":"Wiley","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2012]]},"abstract":"<jats:p>The present paper deals with the various<jats:italic>q<\/jats:italic>-Genocchi numbers and polynomials. We define a new type of multiple generalized<jats:italic>q<\/jats:italic>-Genocchi numbers and polynomials with weight<jats:italic>\u03b1<\/jats:italic>and weak weight<jats:italic>\u03b2<\/jats:italic>by applying the method of<jats:italic>p<\/jats:italic>-adic<jats:italic>q<\/jats:italic>-integral. We will find a link between their numbers and polynomials with weight<jats:italic>\u03b1<\/jats:italic>and weak weight<jats:italic>\u03b2<\/jats:italic>. Also we will obtain the interesting properties of their numbers and polynomials with weight<jats:italic>\u03b1<\/jats:italic>and weak weight<jats:italic>\u03b2<\/jats:italic>. Moreover, we construct a Hurwitz-type zeta function which interpolates multiple generalized<jats:italic>q<\/jats:italic>-Genocchi polynomials with weight<jats:italic>\u03b1<\/jats:italic>and weak weight<jats:italic>\u03b2<\/jats:italic>and find some combinatorial relations.<\/jats:p>","DOI":"10.1155\/2012\/179385","type":"journal-article","created":{"date-parts":[[2012,10,1]],"date-time":"2012-10-01T00:04:47Z","timestamp":1349049887000},"page":"1-13","source":"Crossref","is-referenced-by-count":0,"title":["Some Properties of Multiple Generalized<i>q<\/i>-Genocchi Polynomials with Weight and Weak Weight"],"prefix":"10.1155","volume":"2012","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2663-7101","authenticated-orcid":true,"given":"J. 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