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Several characterizations of bivariate quantum-Hermite-Appell Polynomials and the structure of their zeros

dc.contributor.authorMohra Zayed
dc.contributor.authorTaghreed Alqurashi
dc.contributor.authorShahid Ahmad Wani
dc.contributor.authorCheon Seoung Ryoo
dc.contributor.authorWilliam Ramírez
dc.contributor.otherMathematics Department, College of Science, King Khalid University, Abha 61413, Saudi Arabia
dc.contributor.otherMathematics Department, Faculty of Science, Al-Baha University, 65779-7738 Albaha City, Kingdom of Saudi Arabia
dc.contributor.otherSymbiosis Institute of Technology, Pune Campus, Symbiosis International (Deemed University) (SIU), Pune, Maharashtra, India
dc.contributor.otherDepartment of Mathematics, Hannam University, Daejeon 34430, South Korea
dc.contributor.otherDepartment of Natural and Exact Sciences, Universidad de la Costa, Barranquilla 080002, Colombia
dc.date.accessioned2025-08-27T02:32:15Z
dc.date.accessioned2025-10-08T08:49:28Z
dc.date.available2025-10-08T08:49:28Z
dc.date.issued01-05-2025
dc.identifier.urihttps://www.aimspress.com/article/doi/10.3934/math.2025507
dc.identifier.urihttp://digilib.fisipol.ugm.ac.id/repo/handle/15717717/37488
dc.description.abstractThis paper investigated the fundamental characteristics and uses of a new class of bivariate quantum-Hermite-Appell polynomials. The series representation and generating relation for these polynomials were derived. Also, a determinant representation for these polynomials was derived. Further, important mathematical characteristics were derived, such as $ q $-recurrence relations and $ q $-difference equations. These polynomials' numerical features were methodically examined, providing information on their computational possibilities and the framework of their zeros. A coherent framework was established by extending the study to related families, such as quantum-Hermite Bernoulli, quantum-Hermite Euler, and quantum-Hermite Genocchi polynomials. These discoveries enhance the knowledge of quantum polynomials and their relationships to classical and contemporary special functions.
dc.language.isoEN
dc.publisherAIMS Press
dc.subject.lccMathematics
dc.titleSeveral characterizations of bivariate quantum-Hermite-Appell Polynomials and the structure of their zeros
dc.typeArticle
dc.description.keywordsspecial functions
dc.description.keywordsquantum calculus
dc.description.keywordsexplicit form
dc.description.keywordsoperational connection
dc.description.keywordsstructure of zeros
dc.description.keywordsdeterminant form
dc.description.pages11184-11207
dc.description.doi10.3934/math.2025507
dc.title.journalAIMS Mathematics
dc.identifier.e-issn2473-6988
dc.identifier.oaioai:doaj.org/journal:4e2bbeba283b4bac8495e3dd1ddde5b7
dc.journal.infoVolume 10, Issue 5


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