منابع مشابه
Summation 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...
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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 کاملA note on the summation of an infinite series involving a hypergeometric function
The mathematical properties of the generalized hypergeometric function are now well established, due largely to the efforts of Bailey, Watson, Slater, and many others. There are available a number of books on the subject ['], [6] which contain extensive bibliographies together with an outline of the history of the investigations. A large portion of the published work concerning these functions ...
متن کاملInfinite Series
so π is an “infinite sum” of fractions. Decimal expansions like this show that an infinite series is not a paradoxical idea, although it may not be clear how to deal with non-decimal infinite series like (1.1) at the moment. Infinite series provide two conceptual insights into the nature of the basic functions met in high school (rational functions, trigonometric and inverse trigonometric funct...
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We consider a forced differential difference equation and by the use of Laplace Transform Theory generate non-hypergeometric type series which we prove may be expressed in closed form.
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 1966
ISSN: 0004-9735
DOI: 10.1017/s1446788700004948