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arXiv · 2603.28940

Hypergeometric Bernoulli Polynomials Defined on Simplicial $d$-Polytopic Numbers

Ronald Orozco
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Abstract

We introduce an ${\rm S}_d$-analogue of the hypergeometric Bernoulli polynomials and study their properties. To achieve this goal, we introduce a calculus defined on the simplicial $d$-polytopic numbers. Two definitions of the ${\rm S}_d$-derivatives are given. These two definitions allow us to derive an identity relating Kummer confluent hypergeometric function and Touchard polynomials. This calculus is closely related to the $d$-Hoggatt binomial coefficients. ${\rm S}_d$-analogs of the exponential function and the hypergeometric functions are given.

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BibTeXRIS

Ronald Orozco. 2026-03-30. Hypergeometric Bernoulli Polynomials Defined on Simplicial $d$-Polytopic Numbers. https://arxiv.org/abs/2603.28940

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