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Abstract 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) U (n+1) type generating functions and Ramanujan’s integrals involving general Al-Salam–Carlitz polynomials by q -difference equation.
Cao et al. (Fri,) studied this question.