英语词汇“absolutely convergent”的英英意思、用法、释义、翻译、读音、例句、短语、词组-英语词典

12. Mathematics. With regard to the absolute values of component quantities; absolutely convergent adj. (of an infinite series) such that the series of absolute values of its terms converges; (of an integral) such that the integral of the absolute value of the integrand is finite; cf. absolute convergence n. at absolute adj. and n. Compounds 2.

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1814 T. Leybourn Math. Repository New Ser. III. iii. 13 The second [integral] seems, at first, to depend on functions of the third species; but by a very simple substitution, it will be found absolutely integrable by circular arcs, or by logarithms.

1845 Penny Cycl. Suppl. I. 537/2 The following expression is absolutely integrable, independently of all relation between x and y, if [etc.].

1884 Ann. Math. 1 51 This is not an allowable formula, for it is not absolutely convergent for any value of z, as may be readily shown.

1916 Trans. Amer. Math. Soc. 17 395 The elements of the infinite sequence of matrix products..will certainly converge absolutely and uniformly to the elements of a limit matrix if [etc.].

1965 J. W. Dettman Appl. Complex Variables viii. 365 In the Fourier integral theorem we are dealing with functions which are absolutely integrable, that is ʃ∞−∞|f(t)|dt < ∞.

1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xviii. 396 The series ∑a_n converges absolutely.

2007 Star-Ledger (Newark, New Jersey) (Nexis) 30 Mar. 8 Then came calculus. Such terms as ‘absolutely convergent’ absolutely confused him.

单词	absolutely convergent
释义	> as lemmas absolutely convergent 12. Mathematics. With regard to the absolute values of component quantities; absolutely convergent adj. (of an infinite series) such that the series of absolute values of its terms converges; (of an integral) such that the integral of the absolute value of the integrand is finite; cf. absolute convergence n. at absolute adj. and n. Compounds 2. ΚΠ 1814 T. Leybourn Math. Repository New Ser. III. iii. 13 The second [integral] seems, at first, to depend on functions of the third species; but by a very simple substitution, it will be found absolutely integrable by circular arcs, or by logarithms. 1845 Penny Cycl. Suppl. I. 537/2 The following expression is absolutely integrable, independently of all relation between x and y, if [etc.]. 1884 Ann. Math. 1 51 This is not an allowable formula, for it is not absolutely convergent for any value of z, as may be readily shown. 1916 Trans. Amer. Math. Soc. 17 395 The elements of the infinite sequence of matrix products..will certainly converge absolutely and uniformly to the elements of a limit matrix if [etc.]. 1965 J. W. Dettman Appl. Complex Variables viii. 365 In the Fourier integral theorem we are dealing with functions which are absolutely integrable, that is ʃ∞−∞\|f(t)\|dt < ∞. 1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xviii. 396 The series ∑a_n converges absolutely. 2007 Star-Ledger (Newark, New Jersey) (Nexis) 30 Mar. 8 Then came calculus. Such terms as ‘absolutely convergent’ absolutely confused him. extracted from absolutelyadv.int. < as lemmas
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