Preprint Article Version 1 This version is not peer-reviewed

# Regularized Integral Representations of the Reciprocal Gamma Function

Version 1 : Received: 24 December 2018 / Approved: 25 December 2018 / Online: 25 December 2018 (14:12:56 CET)

A peer-reviewed article of this Preprint also exists.

Prodanov, D. Regularized Integral Representations of the Reciprocal Gamma Function. Fractal Fract 2019, 3, 1. Prodanov, D. Regularized Integral Representations of the Reciprocal Gamma Function. Fractal Fract 2019, 3, 1.

Journal reference: Fractal Fract 2019, 3, 1
DOI: 10.3390/fractalfract3010001

## Abstract

This paper establishes a real integral representation of the reciprocal $\Gamma$ function in terms of a regularized hypersingular integral. The equivalence with the usual complex representation is demonstrated. A regularized complex representation along the usual Hankel path is derived.

## Subject Areas

gamma function; reciprocal gamma function; integral equation