Leading coefficient in the Hankel determinants related to binomial and q-binomial transforms

Key Points

• The leading coefficient in Hankel determinants remains unchanged under binomial transforms, supporting a fundamental property.
• Notably, the degrees of Hankel determinants follow similar patterns to those found in q-binomial cases, showcasing a wider applicability.
• An analytical approach was taken to observe the leading coefficient behavior in even-indexed Bernoulli polynomials with specific binomial transforms.
• Implications of this work emphasize the connections between traditional and q-binomial transforms, enhancing understanding in polynomial theory.