학술논문
Regularized Integral Representations of the Reciprocal Gamma Function
Document Type
article
Author
Source
Fractal and Fractional, Vol 3, Iss 1, p 1 (2019)
Subject
Language
English
ISSN
2504-3110
Abstract
This paper establishes a real integral representation of the reciprocal Gamma function in terms of a regularized hypersingular integral along the real line. A regularized complex representation along the Hankel path is derived. The equivalence with the Heine’s complex representation is demonstrated. For both real and complex integrals, the regularized representation can be expressed in terms of the two-parameter Mittag-Leffler function. Reference numerical implementations in the Computer Algebra System Maxima are provided.