Evaluation of cauchy polynomials via degenerate r -Stirling numbers

In this paper, within the framework of unsigned degenerate [Formula: see text]-Stirling numbers, we establish connections among Cauchy polynomials, degenerate Bernoulli polynomials, and degenerate hyperharmonic numbers. The key results include: (i) expressing the values of Cauchy polynomials at nonnegative integers using the unsigned degenerate [Formula: see text]-Stirling numbers of the first kind, and inverting these expressions via the inversion relation with the degenerate [Formula: see text]-Stirling numbers of the second kind; (ii) representing the values of Cauchy polynomials at nonnegative integers in terms of the values of fully degenerate Bernoulli polynomials, and vice versa, using either kind of degenerate [Formula: see text]-Stirling numbers; (iii) introducing degenerate Cauchy polynomials and deriving an identity that connects them to degenerate hyperharmonic numbers.