کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4624773 1340288 2013 17 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
On gamma quotients and infinite products
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات کاربردی
پیش نمایش صفحه اول مقاله
On gamma quotients and infinite products
چکیده انگلیسی

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 Ramanujanʼs 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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Applied Mathematics - Volume 51, Issue 5, October 2013, Pages 546–562
نویسندگان
, ,