摘要：In this paper, we deduce the generalized q-difference equations for general Al-Salam–Carlitz polynomials and generalize Arjika’s recent results (Arjika in J. Differ. Equ. Appl. 26:987–999, 2020). In addition, we obtain transformational identities by the method of q-difference equation. Moreover, we deduce $U(n 1)$ type generating functions and Ramanujan’s integrals involving general Al-Salam–Carlitz polynomials by q-difference equation.
关键词：q-Difference equation; q-Difference operator; Al-Salam–Carlitz
polynomials; Generating functions; Ramanujan’s integral
