On partial sums of normalized Mittag-Leffler functions

TL;DR

This paper investigates the ratio between the normalized Mittag-Leffler function and its partial sums, providing theoretical results and examples to illustrate their relationships.

Contribution

It introduces new bounds and properties for the ratio of normalized Mittag-Leffler functions and their partial sums.

Findings

Derived inequalities for the ratio of functions and partial sums

Provided illustrative examples validating the theoretical results

Enhanced understanding of Mittag-Leffler function approximations

Abstract

This article deals with the ratio of normalized Mittag-Leffler function $\mathbb{E}_{\alpha,\beta}(z)$ and its sequence of partial sums $(\mathbb{E}_{\alpha,\beta})_m(z)$. Several examples which illustrate the validity of our results are also given.