A Construction That Produces Wallis-Type Formulas
نویسندگان
چکیده
منابع مشابه
Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree Smolyak's Construction of Cubature Formulas of Arbitrary Trigonometric Degree
We study cubature formulas for d-dimensional integrals with a high trigonometric degree. To obtain a trigonometric degreè in dimension d, we need about d ` =`! function values if d is large. Only a small number of arithmetical operations is needed to construct the cubature formulas using Smolyak's technique. We also compare diierent methods to obtain formulas with high trigonometric degree. Abs...
متن کاملOn Wallis-type Products and Pólya's Urn Schemes
A famous “curious identity” of Wallis gives a representation of the constant π in terms of a simply structured infinite product of fractions. Sondow and Yi [Amer. Math. Monthly 117 (2010), 912-917] identified a general scheme for evaluating Wallis-type infinite products. The main purpose of this paper is to discuss an interpretation of the scheme by means of Pólya urn models.
متن کاملWallis Inequality with a Parameter
We introduce a parameter z for the well-known Wallis’ inequality, and improve results on Wallis’ inequality are proposed. Recent results by other authors are also improved.
متن کاملConstruction of Variable-Stepsize Multistep Formulas
A systematic way of extending a general fixed-stepsize multistep formula to a minimum storage variable-stepsize formula has been discovered that encompasses fixed-coefficient (interpolatory), variable-coefficient (variable step), and fixed leading coefficient as special cases. In particular, it is shown that the " interpolatory" stepsize changing technique of Nordsieck leads to a truly variable...
متن کاملConstruction of spherical cubature formulas using lattices
We construct cubature formulas on spheres supported by homothetic images of shells in some Euclidian lattices. Our analysis of these cubature formulas uses results from the theory of modular forms. Examples are worked out on S for n = 4, 8, 12, 14, 16, 20, 23, and 24, and the sizes of the cubature formulas we obtain are compared with the lower bounds given by Linear Programming.
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: Advances in Pure Mathematics
سال: 2013
ISSN: 2160-0368,2160-0384
DOI: 10.4236/apm.2013.36074