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arXiv · 2401.13696

Formulas involving Cauchy polynomials, Bernoulli polynomials, and generalized Stirling numbers

José L. Cereceda
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Abstract

In this paper, we derive novel formulas and identities connecting Cauchy numbers and polynomials with both ordinary and generalized Stirling numbers, binomial coefficients, central factorial numbers, Euler polynomials, $r$-Whitney numbers, and hyperharmonic polynomials, as well as Bernoulli numbers and polynomials. We also provide formulas for the higher-order derivatives of Cauchy polynomials and obtain corresponding formulas and identities for poly-Cauchy polynomials. Furthermore, we introduce a multiparameter framework for poly-Cauchy polynomials, unifying earlier generalizations like shifted poly-Cauchy numbers and polynomials with a $q$ parameter.

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José L. Cereceda. 2024-01-18. Formulas involving Cauchy polynomials, Bernoulli polynomials, and generalized Stirling numbers. https://doi.org/10.3390/axioms14100746

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