Deret (matematika): Perbedaan antara revisi
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Baris 170:
:<math>\int_E \left|s_N(x)-f(x)\right|^2\,dx \to 0</math>
as ''N'' → ∞.
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=== Deret pangkat ===
'''Deret pangkat''' adalah suatu deret dalam bentuk
▲:{{Main|Power series}}
:<math>\sum_{n=0}^\infty a_n(x-c)^n.</math>
[[Deret Taylor]] pada suatu titik ''c'' pada suatu fungsi adalah suatu
:<math>\sum_{n=0}^{\infty} \frac{x^n}{n!}</math>
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Unless it converges only at ''x''=''c'', such a series converges on a certain open disc of convergence centered at the point ''c'' in the complex plane, and may also converge at some of the points of the boundary of the disc. The radius of this disc is known as the [[radius of convergence]], and can in principle be determined from the asymptotics of the coefficients ''a''<sub>''n''</sub>. The convergence is uniform on [[closed set|closed]] and [[bounded set|bounded]] (that is, [[compact set|compact]]) subsets of the interior of the disc of convergence: to wit, it is [[Compact convergence|uniformly convergent on compact sets]].
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