On a Generalization of Bernoulli and Euler Numbers

TL;DR

This paper introduces a new series of numbers generalizing Bernoulli and Euler numbers, explores their properties, and applies them to solve probability problems and propose a statistical test for independence.

Contribution

It presents a novel generalization of classical numbers and demonstrates their application in probability and statistical testing.

Findings

New series of numbers generalizing Bernoulli and Euler numbers.

Application of these numbers to solve probability problems.

Proposal of a statistical test for independence and identical distribution.

Abstract

We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and identical distribution of random variables.