Generalizing Wallis' Formula
نویسنده
چکیده
The present note generalizes Wallis’ formula, 2 = . 7 6 . 5 6 . 5 4 . 3 4 . 3 2 . 1 2 , using the EulerMascheroni constant g and the Glaisher-Kinkelin constant A: 2 ln 2 4 = 3 3 2 . 1 2 . 5 4 3 4
منابع مشابه
√1 1√1
This equation becomes Wallis’ product when p = 0 and Vieta’s formula as p → ∞. It is surprising that such a connection between the two products was not discovered earlier. The collection [1] contains both original papers of Vieta and Wallis as well as other fundamental papers in the history of π. Indeed, there are many good historical sources on π. The text by P. Eymard and J. P. Lafon [6] is a...
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by repeated partial integration. The topic is usually reserved for more advanced calculus courses. The purpose of this note is to show that (1) can be derived using only the mathematics taught in elementary school, that is, basic algebra, the Pythagorean theorem, and the formula π · r 2 for the area of a circle of radius r . Viggo Brun gives an account of Wallis’s method in [1] (in Norwegian). ...
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ورودعنوان ژورنال:
- The American Mathematical Monthly
دوره 122 شماره
صفحات -
تاریخ انتشار 2015