A new entire factorial function

TL;DR

This paper introduces a new entire factorial function that matches the Euler gamma function at positive integers and half-integers, offering a novel mathematical tool with unique properties.

Contribution

The paper presents a new entire factorial function that coincides with the Euler gamma function at key points, expanding the class of factorial-related functions.

Findings

The new function is entire and matches gamma at positive integers and half-integers.

It has unique analytical properties distinguishing it from the classical gamma function.

Basic features and potential applications are described.

Abstract

We introduce a new factorial function which agrees with the usual Euler gamma function at both the positive integers and at all half-integers, but which is also entire. We describe the basic features of this function.