GENERALIZED q-DIFFERENCE EQUATION FOR THE GENERALIZED q-OPERATOR ᵣ????ₛ (Dq) AND ITS APPLICATIONS IN q-INTEGRALS

GENERALIZED q-DIFFERENCE EQUATION FOR THE GENERALIZED q-OPERATOR ᵣ????ₛ (Dq) AND ITS APPLICATIONS IN q-INTEGRALS

F. A. Reshem, H. L. Saad

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Abstract

In 2014, Fang [12] discovered a general q-exponential operator identity by solving a q-di erence equation. Fang [12] developed some generalizations of q-integrals using this q-di erence equation. Reshem and Saad [20] presented the solution to a generalized q-di erence equation in q-operator form, which is a generalization of Fang's work [12]. Using the q-di erence equation technique, Reshem and Saad [20] discussed some properties of q-polynomials. In this paper, the generalized q-di erence equation technique is used to generalize some well-known integrals such as fractional q-integrals, the q-Barnes contour integral, and Ramanujan q-integrals.

Keywords

q-di erence equation, q-operator, q-integral, fractional q-integrals, q-Barnes contour integral, Ramanujan q-integrals