Partial sums of Hyper-Bessel function with applications

TL;DR

This paper establishes lower bounds for ratios involving the hyper-Bessel function and its partial sums, providing insights into their approximation properties and potential applications.

Contribution

It introduces new lower bounds for ratios of the normalized hyper-Bessel function and its derivatives to their partial sums, advancing understanding of their approximation behavior.

Findings

Lower bounds for the quotient of hyper-Bessel function and its partial sum

Lower bounds for the quotient of the derivative of hyper-Bessel function and its partial sum

Applications demonstrating the usefulness of these bounds

Abstract

The main purpose of present paper is to determine some lower bounds for the quotient of the normalized hyper-Bessel function and its partial sum, as well as for the quotient of the derivative of normalized hyper-Bessel function and its partial sum. In addition, some applications related to obtained results are also given.