Next Article in Journal
Acknowledgement to Reviewers of Fractal Fract in 2018
Next Article in Special Issue
Integral Representations and Algebraic Decompositions of the Fox-Wright Type of Special Functions
Previous Article in Journal
Fractal Calculus of Functions on Cantor Tartan Spaces
Previous Article in Special Issue
Mathematical Modeling of Solutes Migration under the Conditions of Groundwater Filtration by the Model with the k-Caputo Fractional Derivative
Open AccessArticle

Regularized Integral Representations of the Reciprocal Gamma Function

1
Environment, Health and Safety, IMEC, 3001 Leuven, Belgium
2
Neuroscience Research Flanders, 3001 Leuven, Belgium
Fractal Fract 2019, 3(1), 1; https://doi.org/10.3390/fractalfract3010001
Received: 16 November 2018 / Revised: 29 December 2018 / Accepted: 8 January 2019 / Published: 12 January 2019
(This article belongs to the Special Issue The Craft of Fractional Modelling in Science and Engineering 2018)
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. View Full-Text
Keywords: Gamma function; reciprocal Gamma function; Mittag-Leffler function; integral equation Gamma function; reciprocal Gamma function; Mittag-Leffler function; integral equation
Show Figures

Figure 1

MDPI and ACS Style

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

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop