<?xml version="1.0" encoding="UTF-8"?><OAI-PMH xmlns="http://www.openarchives.org/OAI/2.0/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/ http://www.openarchives.org/OAI/2.0/OAI-PMH.xsd"><responseDate>2026-10-19T01:11:20Z</responseDate><request verb="GetRecord" identifier="oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/12616" metadataPrefix="oai_dc">https://ebyu-rdlopen.rawdatalibrary.net/oai/request</request><GetRecord><record><header><identifier>oai:ebyu-rdlopen.rawdatalibrary.net:ebyu/12616</identifier><datestamp>2026-10-18T20:36:35Z</datestamp><setSpec>openaire</setSpec><setSpec>driver</setSpec><setSpec>com_ebyu_10000</setSpec><setSpec>col_ebyu_10001</setSpec></header><metadata><oai_dc:dc xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd"><dc:title>Catalan transform of the incomplete Jacobsthal numbers and incomplete generalized Jacobsthal polynomials</dc:title><dc:creator>Özkan, Engi˙n</dc:creator><dc:creator>Uysal, Mi˙ne</dc:creator><dc:creator>Kuloǧlu, Bahar</dc:creator><dc:subject>Binet formula</dc:subject><dc:subject>generating function</dc:subject><dc:subject>h (x)-Jacobsthal polynomials</dc:subject><dc:subject>Hankel transform</dc:subject><dc:subject>incomplete h (x)- Jacobsthal polynomials</dc:subject><dc:description>We introduce the Catalan transform of the Incomplete Jacobsthal numbers. We apply the Hankel transform to the Catalan transforms of these numbers. We calculate determinants of matrixes formed with CJk,nlby using Hankel transform. Then we define the incomplete h(x)-Jacobsthal polynomials. Then we examine the recurrence relation and some properties of these polynomials.  © 2022 World Scientific Publishing Company.</dc:description><dc:publisher>World Scientific</dc:publisher><dc:date>2022</dc:date><dc:type>Article</dc:type><dc:identifier>https://rdlopen.rawdatalibrary.net/r/ebyu/12616</dc:identifier><dc:identifier>https://doi.org/10.1142/s1793557122501194</dc:identifier><dc:identifier>1793-5571</dc:identifier><dc:language>en</dc:language><dc:relation>Asian-European Journal of Mathematics</dc:relation><dc:rights>info:eu-repo/semantics/openAccess</dc:rights><dc:type>info:eu-repo/semantics/article</dc:type><dc:identifier>https://ebyu-rdlopen.rawdatalibrary.net/tr/items/ebyu/12616</dc:identifier></oai_dc:dc></metadata></record></GetRecord></OAI-PMH>