单词 | semi-convergent |
释义 | > as lemmassemi-convergent semi-convergent adj. Brit. /ˌsɛmɪkənˈvəːdʒ(ə)nt/ , U.S. /ˌsɛˌmaɪkənˈvərdʒənt/ , /ˌsɛmikənˈvərdʒənt/ applied to a series the sum of whose terms converges while the sum of the moduli of its terms diverges.ΚΠ 1872 Monthly Notices Royal Astron. Soc. XXXII. 262 Most functions are expansible in an ascending (convergent) series of the form A0 + A1x + A2x2 +…, and a descending (semi-convergent) series of the form B1/x − B2/x2 + B3/x3 −… 1902 E. T. Whittaker Mod. Anal. 12 Series which though convergent are not absolutely convergent (i.e. the series themselves converge, but the series of moduli diverge) are said to be semi-convergent or conditionally convergent. 1959 A. Zygmund Trigonometric Series (ed. 2) II. iv. 175 If f is continuous, and S[f] is uniformly semi-convergent to f from below, then S[f] converges uniformly. < as lemmas |
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