**On gamma quotients and infinite products**

Marc Chamberland, Armin Straub — Advances in Applied Mathematics — Volume 51, Number 5, 2013, Pages 546-562

## Abstract

Infinite products, indexed by all natural numbers, in which each factor is a rational function of the index, can always be evaluated in terms of finite products of gamma functions. This goes back to Euler. A purpose of this note is to demonstrate the usefulness of this fact through a number of diverse applications involving multiplicative partitions, entries in Ramanujan's notebooks, the Chowla--Selberg formula, and the Thue--Morse sequence. In addition, we propose a numerical method for efficiently evaluating more general infinite series such as the slowly convergent Kepler--Bouwkamp constant.**Corrigendum:**
In Example 2.4, "z" needs to be replaced by "-z" on the right-hand side of the first equation.

## Download

Link | Size | Description | Hits |
---|---|---|---|

gammaquotients.pdf | 316.09 KB | Preprint (PDF, 19 pages) | 5179 |

## BibTeX

@article{gammaquotients-2013, author = {Marc Chamberland and Armin Straub}, title = {On gamma quotients and infinite products}, journal = {Advances in Applied Mathematics}, year = {2013}, volume = {51}, number = {5}, pages = {546--562}, doi = {10.1016/j.aam.2013.07.003}, }