Observational analysis reveals behavior of leading coefficients in Hankel determinants for q-binomial transforms, indicating broader implications in polynomial studies.
It is a standard result that the Hankel determinants for a sequence stay invariant after performing the binomial transform on this sequence. In this work, we extend the scenario to q -binomial transforms and study the behavior of the leading coefficient in such Hankel determinants. We also investigate the leading coefficient in the Hankel determinants for even-indexed Bernoulli polynomials with recourse to a curious binomial transform. In particular, the degrees of these Hankel determinants share the same nature as those in one of the q -binomial cases.
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Chern et al. (2026) studied this question.
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