On the generating function of p-Bernoulli numbers: an alternative approach

TL;DR

This paper presents an alternative proof for the generating function of p-Bernoulli numbers using Euler's integral representation, offering a different perspective from previous methods.

Contribution

It introduces a novel proof technique for the generating function of p-Bernoulli numbers based on Euler's integral representation.

Findings

Provides an alternative proof of the generating function.

Utilizes Euler's integral representation for Bernoulli numbers.

Offers a new perspective on p-Bernoulli numbers' generating function.

Abstract

In this note, we give an alternative proof of the generating function of $p$-Bernoulli numbers. Our argument is based on the Euler's integral representation.