Topic
Reciprocal gamma function
About: Reciprocal gamma function is a research topic. Over the lifetime, 16 publications have been published within this topic receiving 147 citations.
Papers
12 Jan 2018
TL;DR: In this article, the real and complex zeros of Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, P\'olya and Runckel.
Abstract: The real and complex zeros of some special entire functions such as Wright, hyper-Bessel, and a special case of generalized hypergeometric functions are studied by using some classical results of Laguerre, Obreschkhoff, P\'olya and Runckel. The obtained results extend the known theorem of Hurwitz on exact number of nonreal zeros of Bessel functions of the first kind. Moreover, results on zeros of derivatives of Bessel functions and cross-product of Bessel functions are also given, which are related to some recent open problems.
24 citations
12 Jan 2019
TL;DR: In this paper, a real integral representation of the reciprocal Gamma function in terms of a regularized hypersingular integral along the real line is derived, and the equivalence with the Heine complex representation is demonstrated.
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.
21 citations
Posted Content•
TL;DR: Using the reflection formula of the Gamma function, a new formula for the Taylor coefficients of the reciprocal Gamma function was derived in this article, which provides effective asymptotic values for the coefficients even for very small values of the indices.
Abstract: Using the reflection formula of the Gamma function, we derive a new formula for the Taylor coefficients of the reciprocal Gamma function. The new formula provides effective asymptotic values for the coefficients even for very small values of the indices. Both the sign oscillations and the leading order of growth are given.
10 citations
6 citations
25 Dec 2018
TL;DR: In this paper, a real integral representation of the reciprocal Gamma function in terms of a regularized hypersingular integral along the real line is derived, and the equivalence with the Heine complex representation is demonstrated.
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.
3 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2019 | 3 |
| 2018 | 6 |
| 2017 | 1 |
| 2014 | 1 |
| 2003 | 1 |