summableadj.

Brit.

/ˈsʌməbl/, U.S.

/ˈsəməb(ə)l/

Origin: Formed within English, by derivation. Etymons: sum v.¹, -able suffix.

Etymology: < sum v.¹ + -able suffix.In sense 2 after French sommable (Henri Lebesgue 1902, in Annali di Matematical 3rd Ser. 7 232).

Mathematics.

a. Of an infinite series (series n. 8): having the property that the sequence of partial sums converges to a definite value, which is taken as the sum of the series; = convergent adj. 2. Also: designating an infinite sequence whose associated series has this property.

ΘΚΠ

the world > relative properties > number > enumeration, reckoning, or calculation > [adjective] > numerable or reckonable

numbrablea1382

numberablea1500

computativea1538

measurable1565

numerable1570

countable1581

accountable1589

computable1610

numerous1638

reckonable1657

summable1718

calculable1742

enumerable1889

scorable1964

1718 A. de Moivre Doctr. Chances Pref. p. ix. The Terms of it will either constitute a Geometric Progression, which by the Known Methods is easily Summable; or else some other sort of Progression.

1784 Philos. Trans. (Royal Soc.) 74 395 Mr. James Bernouilli found summable serieses by assuming a series V.

1862 J. R. Young Course Elem. Math. (ed. 2) 168 It is of importance, therefore, to have some means of ascertaining whether a series, such as this, is convergent, and therefore summable..or whether it is divergent, and therefore not summable.

2009 D. Corbae et al. Introd. Math. Anal. for Econ. Theory & Econometrics iii. 95 The sequence 1, −1, 1, −1,... is not summable as the partial sums of its absolute values are not bounded.

b. Designating an infinite series which, according to any of several criteria other than convergence of its partial sums, may be considered as having a sum.Frequently with distinguishing word, as Abel summable, Cesàro summable, or Euler summable.

ΚΠ

1902 Philos. Trans. (Royal Soc.) A. 199 450 If we treat the series entering into the expression of P( z ) as series which are summable though divergent, the expansion will be independent of n.

1957 Proc. London Math. Soc. 7 456 We cannot assert the convergence of (7) except when r ≥ σ. We can, however, prove that it is Cesàro summable for a wider range of values of r.

2017 M. Laczkovich & V. T. Sós Real Anal. vi. 224 The summable series constitute but a very small subset of the full set of all infinite series.

2. Designating a measurable function for which the Lebesgue integral exists and is finite.A summable function was originally (and equivalently) defined as a function that is such that the limits of two particular infinite series coincide, the shared value of these determining that of the Lebesgue integral.

ΚΠ

1905 Philos. Trans. (Royal Soc.) A. 204 243 In the case of a summable function, therefore, the outer and inner measures of the integral agree, and we may call either the generalised integral of the function.

2008 Theoret. & Math. Physics 156 1354 We found its formal solution in the form of a series in the class of summable functions.

This entry has been updated (OED Third Edition, September 2019; most recently modified version published online March 2022).

单词	summable
释义	summableadj. Brit. /ˈsʌməbl/, U.S. /ˈsəməb(ə)l/ Origin: Formed within English, by derivation. Etymons: sum v.¹, -able suffix. Etymology: < sum v.¹ + -able suffix.In sense 2 after French sommable (Henri Lebesgue 1902, in Annali di Matematical 3rd Ser. 7 232). Mathematics. 1. a. Of an infinite series (series n. 8): having the property that the sequence of partial sums converges to a definite value, which is taken as the sum of the series; = convergent adj. 2. Also: designating an infinite sequence whose associated series has this property. ΘΚΠ the world > relative properties > number > enumeration, reckoning, or calculation > [adjective] > numerable or reckonable numbrablea1382 numberablea1500 computativea1538 measurable1565 numerable1570 countable1581 accountable1589 computable1610 numerous1638 reckonable1657 summable1718 calculable1742 enumerable1889 scorable1964 1718 A. de Moivre Doctr. Chances Pref. p. ix. The Terms of it will either constitute a Geometric Progression, which by the Known Methods is easily Summable; or else some other sort of Progression. 1784 Philos. Trans. (Royal Soc.) 74 395 Mr. James Bernouilli found summable serieses by assuming a series V. 1862 J. R. Young Course Elem. Math. (ed. 2) 168 It is of importance, therefore, to have some means of ascertaining whether a series, such as this, is convergent, and therefore summable..or whether it is divergent, and therefore not summable. 2009 D. Corbae et al. Introd. Math. Anal. for Econ. Theory & Econometrics iii. 95 The sequence 1, −1, 1, −1,... is not summable as the partial sums of its absolute values are not bounded. b. Designating an infinite series which, according to any of several criteria other than convergence of its partial sums, may be considered as having a sum.Frequently with distinguishing word, as Abel summable, Cesàro summable, or Euler summable. ΚΠ 1902 Philos. Trans. (Royal Soc.) A. 199 450 If we treat the series entering into the expression of P( z ) as series which are summable though divergent, the expansion will be independent of n. 1957 Proc. London Math. Soc. 7 456 We cannot assert the convergence of (7) except when r ≥ σ. We can, however, prove that it is Cesàro summable for a wider range of values of r. 2017 M. Laczkovich & V. T. Sós Real Anal. vi. 224 The summable series constitute but a very small subset of the full set of all infinite series. 2. Designating a measurable function for which the Lebesgue integral exists and is finite.A summable function was originally (and equivalently) defined as a function that is such that the limits of two particular infinite series coincide, the shared value of these determining that of the Lebesgue integral. ΚΠ 1905 Philos. Trans. (Royal Soc.) A. 204 243 In the case of a summable function, therefore, the outer and inner measures of the integral agree, and we may call either the generalised integral of the function. 2008 Theoret. & Math. Physics 156 1354 We found its formal solution in the form of a series in the class of summable functions. This entry has been updated (OED Third Edition, September 2019; most recently modified version published online March 2022). < adj.1718
随便看	oligosideric oligosiderite oligospermia oligospermic oligospermous oligosporean oligosporous oligostemonous oligosyllabic oligosyllable oligotokous oligotrich oligotroph oligotrophic oligotrophication oligotrophies oligotrophy oligotropic oligozoospermia oliguresia oliguria oligurias oliguric olim oline