On gamma quotients and infinite products

被引：19
作者：
Chamberland, Marc [1 ]
Straub, Armin [2 ,3 ]
机构：
[1] Grinnell Coll, Dept Math & Stat, Grinnell, IA 50112 USA
[2] Univ Illinois, Dept Math, Urbana, IL USA
[3] Max Planck Inst Math, D-53111 Bonn, Germany
来源：
ADVANCES IN APPLIED MATHEMATICS | 2013年 / 51卷 / 05期
关键词：
Infinite products; Gamma function; Kepler-Bouwkamp constant; Chowla-Selberg formula; Thue-Morse sequence;
D O I：
10.1016/j.aam.2013.07.003
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Convergent 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. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：546 / 562
页数：17
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