زانکۆی گەرمیانJournal of Garmian University231000876SCAPAS Conferance20190401(Application of the operator 3Ф2 (a,b,c, q, ƒƟ) d,e1891779970410.24271/jgu.2019.99704KURasha H.JaberDepartment of Mathematics, College of Science, Basrah University, Basra, IraqHusam L.SaasDepartment of Mathematics, College of Science, Basrah University, Basra, IraqJournal Article20191226In this paper, we construct the -exponential operator. We use the operator to obtain an extension of Euler identities, Ramanujan’s sum, -Chu- Vanermonde summation formula and we give some other identities. Also we use the operator to get an extension of the Ramanujan’s identity, the Askey beta integral, Ramanujan’s beta integral and we give some other integrals formulas. <em> </em>https://jgu.garmian.edu.krd/article_99704_a6937c5101a5c22623be646cef77b26b.pdf