منابع مشابه
Closed-form Summation of Some Trigonometric Series
The problem of numerical evaluation of the classical trigonometric series ^ sin(2fr+ l)a . ^ cOS(2/c + l)a ¿„(a) = > ——;-—— ana C„(a) = > —rr-,-t;—» £j (2k+1)" ÍTo Vk+XY where v > 1 in the case of Sin(a) and C2„+X(a) with n = 1, 2, 3, ... has been recently addressed by Dempsey, Liu, and Dempsey; Boersma and Dempsey; and by Gautschi. We show that, when a is equal to a rational multiple of 2k , t...
متن کاملMethod of summation of some slowly convergent series
A new method of summation of slowly convergent series is proposed. It may be successfully applied to the summation of generalized and basic hypergeometric series, as well as some classical orthogonal polynomial series expansions. In some special cases, our algorithm is equivalent to Wynn’s epsilon algorithm, Weniger transformation (Computer Physics Reports 10 (1989) 189371) or the technique rec...
متن کاملOn q-Operators and Summation of Some q-Series
Using Jackson's q-derivative and the q-Stirling numbers, we establish some transformation theorems leading to the values of some convergent q-series.
متن کاملSummation of Fourier Series
A general summability method of different orthogonal series is given with the help of an integrable function θ. As special cases the trigonometric Fourier, Walsh-, Walsh-Kaczmarz-, Vilenkinand Ciesielski-Fourier series and the Fourier transforms are considered. For each orthonormal system a different Hardy space is introduced and the atomic decomposition of these Hardy spaces are presented. A s...
متن کاملSummation Notation and Series
Corresponding material in the book: Section 12.1, 12.2, 12.3. What students should definitely get: The summation notation and how it works, series, concepts of convergence. The use of telescoping and forward difference operator ideas to sum up series. The use of the integral test and other tests to determine whether a series converges and obtain numerical estimates. Convergence rules for ration...
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: Applicationes Mathematicae
سال: 1988
ISSN: 1233-7234,1730-6280
DOI: 10.4064/am-20-2-291-297