A determinant approach for generalized q-Bernoulli polynomials and asymptotic results

Key Points

• The aim is to derive determinant representations for generalized q-Bernoulli polynomials and explore their asymptotic behavior.
• Introduced three families of polynomials with generating functions based on Jackson q-analogs of the Bessel function.
• Derived large n asymptotic results for each family of polynomials.
• Developed two expansion theorems for specific classes of entire functions.
• Established a determinant representation for each family of polynomials.
• Provided asymptotic results that describe the behavior of the polynomials as n approaches infinity.
• Presented examples to illustrate the application of the developed theories.