# Ramanujan-Bernoulli numbers as moments of Racah polynomials

## TL;DR

This paper explores the connection between Ramanujan-Bernoulli numbers and Racah polynomials, revealing that these rational numbers can be represented as moments of orthogonal polynomials, extending classical Bernoulli number properties.

## Contribution

It establishes a new link between Ramanujan-Bernoulli numbers and Racah polynomials, showing they serve as moments of these orthogonal polynomials, similar to classical Bernoulli numbers.

## Key findings

- Ramanujan-Bernoulli numbers are moments of Racah polynomials
- Extension of classical Bernoulli number properties to new rational sequences
- New orthogonal polynomial representations for special rational numbers

## Abstract

The classical sequence of Bernoulli numbers is known to the the sequence of moments of a family of orthogonal polynomials. Some similar statements are obtained for another sequence of rational numbers, which is similar in many ways to the Bernoulli numbers.