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<p>Over the last several years, a number of authors have introduced and investigated several types of the parametric polynomials (for example, parametric Bernoulli and Apostol-Bernoulli polynomials, parametric Euler and Apostol-Euler polynomials, parametric Genocchi and Apostol-Genocchi polynomials etc) by making use of the exponential and trigonometric functions. In a sequel, in this paper, we present a new family of the parametric Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi and Fubini type polynomials by utilizing the Bessel function of the first kind. We also investigate some fundamental properties of our introduced polynomials. Moreover, few applications of our defined parametric polynomials with the well-known generalized Voigt functions are pointed out.</p>

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New Families of the Parametric Polynomials and Their Associated Properties

  • 期刊论文

  • 发表日期：

    2025年10月3日

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  • Mohd Ghayasuddin,
  • Nabiullah Khan

摘要

Over the last several years, a number of authors have introduced and investigated several types of the parametric polynomials (for example, parametric Bernoulli and Apostol-Bernoulli polynomials, parametric Euler and Apostol-Euler polynomials, parametric Genocchi and Apostol-Genocchi polynomials etc) by making use of the exponential and trigonometric functions. In a sequel, in this paper, we present a new family of the parametric Apostol-Bernoulli, Apostol-Euler, Apostol-Genocchi and Fubini type polynomials by utilizing the Bessel function of the first kind. We also investigate some fundamental properties of our introduced polynomials. Moreover, few applications of our defined parametric polynomials with the well-known generalized Voigt functions are pointed out.