A two-way infinite series for Lebesgue integrals
نویسندگان
چکیده
منابع مشابه
Infinite Series Forms of Double Integrals
where 1 2 1 2 , , , r r θ θ are any real numbers, and n is any positive integer. We can obtain the infinite series forms of these double integrals using Taylor series expansions and integration term by term theorem; these are the major results of this paper (i.e., Theorems 1-3). Adams et al. [1], Nyblom [2], and Oster [3] provided some techniques to solve the integral problems. Yu [4-29], Yu an...
متن کاملThe Riemann and Lebesgue Integrals
§1 Preliminaries: Step Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 §2 Riemann Integrable Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 §3 Lebesgue measure zero . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 §4 Definition and Properties of the Lebesgue Integral . . . . . . . . . . 7 §5 The spaces L(R) and L(R) ....
متن کاملTwo New Classes of Nonlinear Transformations for Accelerating the Convergence of Infinite Integrals and Series
Two new classes of nonlinear transformations, the Dtransformation to accelerate the convergence of infinite integrals and the d-transformation to accelerate the convergence of infinite series, are presented. In the course of the development of these transformations two interesting asymptotic expansions, one for infinite integrals and the other for infinite series, are derived. The transformatio...
متن کاملa cauchy-schwarz type inequality for fuzzy integrals
نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.
15 صفحه اولThe d2-transformation for infinite double series and the D2-transformation for infinite double integrals
New transformations for accelerating the convergence of infinite double series and infinite double integrals are presented. These transformations are generalizations of the univariate dand D-transformations. The D2transformation for infinite double integrals is efficient if the integrand satisfies a p.d.e. of a certain type. Similarly, the d2-transformation for double series works well for seri...
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: Bulletin of the American Mathematical Society
سال: 1922
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1922-03503-3