期刊
FRACTAL AND FRACTIONAL
卷 3, 期 1, 页码 -出版社
MDPI
DOI: 10.3390/fractalfract3010001
关键词
Gamma function; reciprocal Gamma function; Mittag-Leffler function; integral equation
资金
- Research Fund-Flanders (FWO) [VS. 097.16N]
- COST Association Action [CA16212 INDEPTH]
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.
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