Ioana Petkova

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 4, Pages 104—115

DOI: 10.7546/nntdm.2021.27.4.104-115

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## Details

### Authors and affiliations

Ioana Petkova

*Faculty of Mathematics and Informatics, Sofia University
Sofia, Bulgaria*

### Abstract

In this paper we give representations for the coefficients of the Maclaurin series for and its reciprocal (where is Euler’s Gamma function) with the help of a differential operator , the exponential function and a linear functional (in Theorem 3.1). As a result we obtain the following representations for (in Theorem 3.2):

Theorem 3.1 and Theorem 3.2 are our main results. With the help of the first theorem we give our approach for finding the coefficients of Maclaurin series for and its reciprocal in an explicit form.

### Keywords

- Gamma function
- Zeta function
- Euler’s constant
- Maclaurin series

### 2020 Mathematics Subject Classification

- 33B15
- 11M06
- 30D10
- 30D30
- 30K05
- 41A58

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## Cite this paper

Petkova, I. (2021). Series expansion of the Gamma function and its reciprocal. Notes on Number Theory and Discrete Mathematics, 27(4), 104-115, doi: 10.7546/nntdm.2021.27.4.104-115.