Quantum mechanical derivation of the Wallis formula forπ
نویسندگان
چکیده
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
متن کاملMechanical Formula Derivation in Elementary Geometries
A precise formulation for the relations among certain variables under a set of polynomial equations and a set of polynomial inequations (to exclude certain special cases which cannot be excluded by the selection of parameters alone) is given. Several methods are presented to find such relations. The methods have been implemented and used to find geometry formulas, to discover geometry theorems,...
متن کاملPadé approximant related to the Wallis formula
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). ...
متن کاملAppendix: derivation of sensitivity formula
N=number of women having triple test; p=prevalence of Down's syndrome; p*N=total number of fetuses with Down's syndrome; DR=detection rate; FPR=false positive rate; p*N*DR*AR=number of women with true positive results who have amniocentesis; (1-p)*N*FPR*AR=number of women with false positive results who have amniocentesis; p*N*DR*AR=number having an abortion (all positive amniocentesis results)...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2015
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.4930800