Abstract
We show that there is a concept of q-translation behind the approach used by Liu to prove summation and transformation identities for q-series.We revisit the q-translation associated with the Askey–Wilson operator introduced in Ismail (Ann Comb 5(3–4):347–362, 2001), simplify its formalism and point out new properties of this translation operator.
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Aslan, H., Ismail, M.E.H. (2021). A q-Translation Approach to Liu’s Calculus. In: Alladi, K., Berndt, B.C., Paule, P., Sellers, J.A., Yee, A.J. (eds) George E. Andrews 80 Years of Combinatory Analysis. Trends in Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-57050-7_7
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DOI: https://doi.org/10.1007/978-3-030-57050-7_7
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Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-030-57049-1
Online ISBN: 978-3-030-57050-7
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