Extension of Summation Formulas involving Stirling series

TL;DR

This paper introduces a new family of rapidly convergent summation formulas for finite sums of the form f(k) over positive real bounds, improving computational efficiency.

Contribution

It extends summation formulas involving Stirling series, providing faster convergence methods for finite sums with potential applications in numerical analysis.

Findings

Derived new summation formulas with rapid convergence

Applicable to a wide class of functions f(k)

Enhances computational efficiency for finite sums

Abstract

This paper presents a family of rapidly convergent summation formulas for various finite sums of the form $\sum_{k=0}^{\lfloor x\rfloor}f(k)$, where $x$ is a positive real number.