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<p>In this article, we first introduce the degenerate Bernoulli–Fibonacci numbers and degenerate Euler–Fibonacci numbers. Using these definitions, we then define the degenerate Bernoulli–Fibonacci polynomials and degenerate Euler–Fibonacci polynomials and examine their graphs for several initial values of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40627_2025_170_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\lambda \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>λ</mi> </math></EquationSource> </InlineEquation>. Subsequently, we define the degenerate Bernoulli and Euler <i>F</i>-polynomials and derive new exponential generating functions for these polynomials. Additionally, we investigate various identities associated with these polynomials.</p>

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Degenerate Bernoulli–Fibonacci and Euler–Fibonacci polynomials

  • 期刊论文

  • 发表日期：

    2025年9月25日

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  • Orhan Dişkaya

摘要

In this article, we first introduce the degenerate Bernoulli–Fibonacci numbers and degenerate Euler–Fibonacci numbers. Using these definitions, we then define the degenerate Bernoulli–Fibonacci polynomials and degenerate Euler–Fibonacci polynomials and examine their graphs for several initial values of \(\lambda \) λ . Subsequently, we define the degenerate Bernoulli and Euler F-polynomials and derive new exponential generating functions for these polynomials. Additionally, we investigate various identities associated with these polynomials.