In mathematics, Dirichlet's test is a method of testing for the convergence of a series that is especially useful for proving conditional convergence. |
| Признак Дирихле |  |
Признак Дирихле — теорема, указывающая достаточные условия сходимости несобственных интегралов и суммируемости бесконечных рядов. Названа в честь немецкого математика Лежёна Дирихле. Википедия
The Dirichlet Test. Theorem (The Dirichlet Test) Let X be a metric space. If the functions fn : X → C, gn : X → IR, n ∈ IN obey. ◦ Fn(x) = n. P m=1 fm(x) ... |
Dirichlet's test, in analysis (a branch of mathematics), a test for determining if an infinite series converges to some finite value. The test was devised ... |
17 июл. 2023 г. · The key is that if the terms of the sum are always less (in absolute value) than the terms of some geometric series, then our sum must converge. |
Let's now look at some examples of using Dirichlet's test. Example 1: Show that $\displaystyle{\sum_{n=2}^{\infty} \frac{\cos(n\pi)}{\ln n}}$ converges. |
2 мая 2023 г. · Weierstrass's test is useful and important, but it has a basic shortcoming: it applies only to absolutely uniformly convergent improper ... |
In mathematics, the Dirichlet–Jordan test gives sufficient conditions for a real-valued, periodic function f to be equal to the sum of its Fourier series at ... |
10 нояб. 2023 г. · Stein invites readers first to prove the summation by parts formula and then use it to prove Dirichlet's test for convergence. 2 The summation ... |
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