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<p>This paper introduces Apostol-type Fibonacci matrix polynomials, which extend classical Bernoulli, Euler, and Genocchi polynomials to matrices using the Golden calculus framework. We define two parametric forms involving trigonometric matrix functions. We establish their main properties, including derivative rules, recurrence relations, and summation formulas. Numerical examples demonstrate their practical implementation. This work connects special function theory with matrix analysis, providing new tools for potential applications.</p>

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Apostol Bernoulli-Fibonacci, Euler-Fibonacci, and Genocchi-Fibonacci matrix polynomials via golden fibonacci calculus

  • 期刊论文

  • 发表日期：

    2025年12月6日

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  • Efruz Özlem Mersin,
  • Mustafa Bahşi

摘要

This paper introduces Apostol-type Fibonacci matrix polynomials, which extend classical Bernoulli, Euler, and Genocchi polynomials to matrices using the Golden calculus framework. We define two parametric forms involving trigonometric matrix functions. We establish their main properties, including derivative rules, recurrence relations, and summation formulas. Numerical examples demonstrate their practical implementation. This work connects special function theory with matrix analysis, providing new tools for potential applications.