Moments of Partitions and Derivatives of Higher Order

TL;DR

This paper introduces the concept of moments of integer partitions and demonstrates their appearance in higher order derivatives of specific function combinations, revealing new mathematical relationships.

Contribution

It defines moments of partitions and connects them to higher order derivatives, providing novel insights into combinatorial and analytical function interactions.

Findings

Moments of partitions are linked to derivatives of functions.

Higher order derivatives can be expressed using partition moments.

The work uncovers new mathematical identities involving partitions and derivatives.

Abstract

We Define moments of partitions of integers, and show that they appear in higher order derivatives of certain combinations of functions.