Equivalent series theorem and obtaining some new summable numerical series using fast expansion polynomials
نویسندگان
چکیده
منابع مشابه
Summable series and the Riemann rearrangement theorem
Let N be the set of positive integers. A function from N to a set is called a sequence. If X is a topological space and x ∈ X, a sequence a : N → X is said to converge to x if for every open neighborhood U of x there is some NU such that n ≥ NU implies that an ∈ U . If there is no x ∈ X for which a converges to x, we say that a diverges. Let a : N→ R. We define s(a) : N→ R by sn(a) = ∑n k=1 ak....
متن کاملIntegrals and Summable Trigonometric Series
is that of suitably defining a trigonometric integral with the property that, if the series (1.1) converges everywhere to a function ƒ(x), then f(x) is necessarily integrable and the coefficients, an and bn, given in the usual Fourier form. It is well known that a series may converge everywhere to a function which is not Lebesgue summable nor even Denjoy integrable (completely totalisable, [3])...
متن کاملNUMERICAL APPROACH TO SOLVE SINGULAR INTEGRAL EQUATIONS USING BPFS AND TAYLOR SERIES EXPANSION
In this paper, we give a numerical approach for approximating the solution of second kind Volterra integral equation with Logarithmic kernel using Block Pulse Functions (BPFs) and Taylor series expansion. Also, error analysis shows efficiency and applicability of the presented method. Finally, some numerical examples with exact solution are given.
متن کاملChebyshev Series Expansion of Inverse Polynomials
if the polynomial has no roots in [−1, 1]. If the inverse polynomial is decomposed into partial fractions, the an are linear combinations of simple functions of the polynomial roots. If the first k of the coefficients an are known, the others become linear combinations of these with expansion coefficients derived recursively from the bj ’s. On a closely related theme, finding a polynomial with ...
متن کاملNew Expansion and Infinite Series
Different from the Taylor polynomials, a new formula for function expansion is proposed where the terms are not polynomials. A new infinite series based on the new formula is also proposed, and the new infinite series can keep some important properties of the original functions. Some forms of remainder are also presented for analysis of convergence. In order to show some internal relationships ...
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 Physics: Conference Series
سال: 2021
ISSN: 1742-6588,1742-6596
DOI: 10.1088/1742-6596/1902/1/012027