# The Hydrogen Atom, Pi and Lerch's Transcendent

## TL;DR

This paper explores a mathematical connection linking the hydrogen atom, fundamental constants pi and e, through Lerch's transcendent, revealing new insights into their interrelations.

## Contribution

It introduces a novel link between the hydrogen atom, pi, e, and Lerch's transcendent, expanding understanding of their mathematical relationships.

## Key findings

- Established a connection between hydrogen atom and pi via Lerch's transcendent
- Extended the relationship to include the number e
- Provided new mathematical insights into fundamental constants

## Abstract

In this note, we extend the connection between the hydrogen atom and $\pi$ to the number $e$ via the Lerch's transcendent.