Regularized Integral Representations of the Reciprocal Gamma Function

Fractal and Fractional

卷:3

Dimiter Prodanov¹ 

[1] Environment, Health and Safety, IMEC, 3001 Leuven, Belgium;

关键词: Gamma function;    reciprocal Gamma function;    Mittag-Leffler function;    integral equation;   

DOI  :  10.3390/fractalfract3010001

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown