منابع مشابه
Generalizing Wallis' Formula
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
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Based on the Padé approximation method, in this paper we determine the coefficients [Formula: see text] and [Formula: see text] such that [Formula: see text] where [Formula: see text] is any given integer. Based on the obtained result, we establish a more accurate formula for approximating π, which refines some known results.
متن کاملAn Elementary Proof of the Wallis Product Formula for pi
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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We generalize Schwinger’s original mass formula to the case of an additional isosinglet which mixes with the nonet mesons, by considering the corresponding 3×3 mass matrix in the most general case. We then make further generalization to either (i) an arbitrary number of additional isosinglets mixing with nonet mesons, or (ii) an arbitrary number of mesons with common J mixing with an additional...
متن کاملThe Generalized Tilt Formula
A convex hull consmaction in Minkowski space defines a canonical cell decomposition for a cusped hyperbolic n-manifold. An algorithm to compute the canonical cell decomposition uses the concept of the 'tilt' of an n-simplex relative to each of its (n 1)-dimensional faces. An essential tool for computing tilts is the tilt theorem. The tilt theorem was previously known only in dimensions n < 3, a...
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ژورنال
عنوان ژورنال: Applied Mathematics
سال: 2018
ISSN: 2152-7385,2152-7393
DOI: 10.4236/am.2018.93015