A note on generalized q-difference equations for general Al-Salam--Carlitz polynomials
Abstract
In this paper, we deduce the generalized q-difference equations for general Al-Salam--Carlitz polynomials and generalize Arjika's recently results [q-difference equation for homogeneous q-difference operators and their applications, 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.
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