Absolute convergence

In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute value of the summand is finite. More precisely, a real or complex series $\textstyle\sum_{n=0}^\infty a_n$ is said to converge absolutely if $\textstyle\sum_{n=0}^\infty \left|a_n\right| = L$ for some real number $\textstyle L$ . Similarly, an improper integral of a function, $\textstyle\int_0^\infty f(x)\,dx$ , is said to converge absolutely if the integral of the absolute value of the integrand is finite—that is, if $\textstyle\int_0^\infty \left|f(x)\right|dx = L.$

单词	Absolutely summable
释义	Absolutely summable 英语例句库 This paper presents the source coding theorem for discrete-time stationary Gaussian sources with absolutely summable autocorrelation sequence. 摘要本论文提出具有绝对可加性自相关数列的离散时间稳定高斯讯号的编码定理。英语百科 Absolute convergence In mathematics, an infinite series of numbers is said to converge absolutely (or to be absolutely convergent) if the sum of the absolute value of the summand is finite. More precisely, a real or complex series $\textstyle\sum_{n=0}^\infty a_n$ is said to converge absolutely if $\textstyle\sum_{n=0}^\infty \left\|a_n\right\| = L$ for some real number $\textstyle L$ . Similarly, an improper integral of a function, $\textstyle\int_0^\infty f(x)\,dx$ , is said to converge absolutely if the integral of the absolute value of the integrand is finite—that is, if $\textstyle\int_0^\infty \left\|f(x)\right\|dx = L.$
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Absolutely summable

Absolute convergence