A Note on Jain basis functions

TL;DR

This paper develops moments for Jain basis functions up to the tenth order, revealing their polynomial nature and connections to known integer sequences.

Contribution

It provides explicit polynomial expressions for moments of Jain basis functions and links their coefficients to OEIS sequences, enhancing understanding of their structure.

Findings

Moments are polynomials in one variable with polynomial coefficients.

Polynomial coefficients are connected to OEIS integer sequences.

Explicit formulas for moments up to order ten are derived.

Abstract

In the present article the moments associated with the Jain basis functions are developed to order ten. The moments are shown to be polynomials in one variable with polynomial coefficients. The polynomial coefficients are investigated and shown to be linked to sequences found in the On-line Encyclopedia of Integer Sequences.