جۆری توێژینه‌وه‌ : Original Article

نوسه‌ران

• Rasha H. Jaber
• Husam L. Saas

Department of Mathematics, College of Science, Basrah University, Basra, Iraq

پوخته‌

In 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.    

وشه‌ بنچینه‌ییه‌كان

• the q-exponential operator
• Euler identity
• Ramanujan’s sum
• q-Chu-Vanermonde summation
• the Askey beta integral
• Ramanujan’s identity
• Ramanujan’s beta integral