{"title":"q 微分方程和 q 运算器 _r Φ_s (θ) 在 q 多项式中的应用","authors":"Faiz A. Reshem, Husam L. Saad","doi":"10.24996/ijs.2024.65.3.24","DOIUrl":null,"url":null,"abstract":" We provide a q-operator form solution to a generalized q-difference equation involving (r+s+2)-variables. We introduce a q-polynomials Ψ_n^((A,B)) (x,y,c|q). The generating function, two Rogers formulas, and two types of Srivastava-Agarwal generating functions for the polynomials Ψ_n^((A,B)) (x,y,c|q) are established using the q-difference equation technique.","PeriodicalId":14698,"journal":{"name":"Iraqi Journal of Science","volume":"66 19","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Applications of q-Difference Equation and q-Operator _r Φ_s (θ) in q-Polynomials\",\"authors\":\"Faiz A. Reshem, Husam L. Saad\",\"doi\":\"10.24996/ijs.2024.65.3.24\",\"DOIUrl\":null,\"url\":null,\"abstract\":\" We provide a q-operator form solution to a generalized q-difference equation involving (r+s+2)-variables. We introduce a q-polynomials Ψ_n^((A,B)) (x,y,c|q). The generating function, two Rogers formulas, and two types of Srivastava-Agarwal generating functions for the polynomials Ψ_n^((A,B)) (x,y,c|q) are established using the q-difference equation technique.\",\"PeriodicalId\":14698,\"journal\":{\"name\":\"Iraqi Journal of Science\",\"volume\":\"66 19\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Iraqi Journal of Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24996/ijs.2024.65.3.24\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Earth and Planetary Sciences\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iraqi Journal of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24996/ijs.2024.65.3.24","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Earth and Planetary Sciences","Score":null,"Total":0}
Applications of q-Difference Equation and q-Operator _r Φ_s (θ) in q-Polynomials
We provide a q-operator form solution to a generalized q-difference equation involving (r+s+2)-variables. We introduce a q-polynomials Ψ_n^((A,B)) (x,y,c|q). The generating function, two Rogers formulas, and two types of Srivastava-Agarwal generating functions for the polynomials Ψ_n^((A,B)) (x,y,c|q) are established using the q-difference equation technique.
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