Abstract In 1985, Howard introduced degenerate Cauchy polynomials together with degenerate Bernoulli polynomials. His degenerate Bernoulli polynomials have been studied by many authors, but his degenerate Cauchy polynomials have been forgotten. In this paper, we introduce some kinds of hypergeometric degenerate Cauchy numbers and polynomials from the different viewpoints. By studying the properties of the first one, we give their expressions and determine the coefficients. Concerning the second one, called H-degenerate Cauchy polynomials, we show several identities and study zeta functions interpolating these polynomials.

中文翻译：

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两类超几何退化柯西数

摘要 1985 年，Howard 将退化的柯西多项式与退化的伯努利多项式一起引入。许多作者研究了他的退化伯努利多项式，但他的退化柯西多项式却被遗忘了。在本文中，我们从不同的角度介绍了一些超几何退化柯西数和多项式。通过研究第一个的性质，我们给出它们的表达式并确定系数。关于第二个，称为 H 退化柯西多项式，我们展示了几个恒等式并研究了对这些多项式进行插值的 zeta 函数。