In this study, the \(\omega \) -extension of the usual Bernoulli polynomials of the second type is examined and then examine few of their characteristics and interactions. Additionally, the research introduces advanced \(\omega \) -Bernoulli polynomials of the second type, uncovering various connections and formulas that linked to the Stirling numbers of the first type, the Stirling and central Stirling numbers of the second type, and the degenerate Daehee and Bernoulli polynomials of the second type. The proposed research provides a comprehensive analysis of these mathematical constructs, revealing new insights and relationships within the field.

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A Study on \(\omega \) -Bernoulli Polynomials: Second-Kind Extensions

  • Waseem Ahmad Khan,
  • Azhar Iqbal,
  • Ugur Duran

摘要

In this study, the \(\omega \) -extension of the usual Bernoulli polynomials of the second type is examined and then examine few of their characteristics and interactions. Additionally, the research introduces advanced \(\omega \) -Bernoulli polynomials of the second type, uncovering various connections and formulas that linked to the Stirling numbers of the first type, the Stirling and central Stirling numbers of the second type, and the degenerate Daehee and Bernoulli polynomials of the second type. The proposed research provides a comprehensive analysis of these mathematical constructs, revealing new insights and relationships within the field.