summatoryadj.

Brit.

/ˈsʌmət(ə)ri/, U.S.

/ˈsəməˌtɔri/

Origin: A borrowing from Latin. Etymon: Latin summatorius.

Etymology: < post-classical Latin summatorius (1682 or earlier in a mathematical context) < summat- , past participial stem of summare (see summate v.) + classical Latin -ōrius -ory suffix².

Mathematics.

†1.

a. summatory arithmetic n. Obsolete rare = summatory calculus n. at sense 1b.

ΘΚΠ

the world > relative properties > number > calculus > [noun]

calculus1672

fluxions1702

summatory calculus1704

infinitesimal calculus1801

rheometry1841

1704 C. Hayes Treat. Fluxions 60 The fundamental Rule in Summatory Arithmetick, to find the Flowing Quantity of a given Fluxion.

b. summatory calculus n. Obsolete the branch of calculus concerned with the finding of integrals (integral n. 4(a)) and study of their properties; the integral calculus.

ΚΠ

1710 J. Harris Lexicon Technicum II Summatory Calculus, according to some, is the same with the Calculus Differentialis of Leibnitz; but more properly Summatory Arithmetick, is the Art of finding the flowing Quantity, from the Fluxion.

1811 Port-Folio 6 6 Your observations, on the science of Fluxions, particularly the Summatory Calculus, have induced me..to bestow more than ordinary attention on that subject.

1917 Monist 27 440 These are the elementary principles of the differential and summatory calculus.

2. Concerning, involving, or relating to summation. Somewhat rare.

ΚΠ

1765 Baxter's Matho (ed. 3) II. x. 273 I imagine there are summatory methods of collecting all those small motions into one aggregate.

1845 Cambr. Math. Jrnl. 4 197 If in the same formulæ we omit the corresponding marks (.), summatory signs, and terms of the series L, M, N.., the resulting equations are still true.

1931 Jrnl. London Math. Soc. 6 63 Plana's summatory formula is not applicable to either of the results.

1986 Communications Statistics—Simulation & Computation 15 701 In the present case we ignore the possibility of asymptotic nuisance terms.., and carry out a validity study using several approaches to the summatory problem.

3. Designating an arithmetic function whose value at a given integer n is the sum of the values of another arithmetic function when evaluated at every element of its domain that is less than or equal to n.

ΚΠ

1913 Trans. Amer. Math. Soc. 14 113 Formerly the research of asymptotic expressions in the theory of numbers was largely confined to the approximate determination of the summatory function (or the mean value) of a given arithmetic function.

2014 M. Overholt Course Anal. Number Theory i. 23 To calculate a local average by differencing an estimate for the associated summatory function is not always efficient.

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

单词	summatory
释义	summatoryadj. Brit. /ˈsʌmət(ə)ri/, U.S. /ˈsəməˌtɔri/ Origin: A borrowing from Latin. Etymon: Latin summatorius. Etymology: < post-classical Latin summatorius (1682 or earlier in a mathematical context) < summat- , past participial stem of summare (see summate v.) + classical Latin -ōrius -ory suffix². Mathematics. †1. a. summatory arithmetic n. Obsolete rare = summatory calculus n. at sense 1b. ΘΚΠ the world > relative properties > number > calculus > [noun] calculus1672 fluxions1702 summatory calculus1704 infinitesimal calculus1801 rheometry1841 1704 C. Hayes Treat. Fluxions 60 The fundamental Rule in Summatory Arithmetick, to find the Flowing Quantity of a given Fluxion. b. summatory calculus n. Obsolete the branch of calculus concerned with the finding of integrals (integral n. 4(a)) and study of their properties; the integral calculus. ΚΠ 1710 J. Harris Lexicon Technicum II Summatory Calculus, according to some, is the same with the Calculus Differentialis of Leibnitz; but more properly Summatory Arithmetick, is the Art of finding the flowing Quantity, from the Fluxion. 1811 Port-Folio 6 6 Your observations, on the science of Fluxions, particularly the Summatory Calculus, have induced me..to bestow more than ordinary attention on that subject. 1917 Monist 27 440 These are the elementary principles of the differential and summatory calculus. 2. Concerning, involving, or relating to summation. Somewhat rare. ΚΠ 1765 Baxter's Matho (ed. 3) II. x. 273 I imagine there are summatory methods of collecting all those small motions into one aggregate. 1845 Cambr. Math. Jrnl. 4 197 If in the same formulæ we omit the corresponding marks (.), summatory signs, and terms of the series L, M, N.., the resulting equations are still true. 1931 Jrnl. London Math. Soc. 6 63 Plana's summatory formula is not applicable to either of the results. 1986 Communications Statistics—Simulation & Computation 15 701 In the present case we ignore the possibility of asymptotic nuisance terms.., and carry out a validity study using several approaches to the summatory problem. 3. Designating an arithmetic function whose value at a given integer n is the sum of the values of another arithmetic function when evaluated at every element of its domain that is less than or equal to n. ΚΠ 1913 Trans. Amer. Math. Soc. 14 113 Formerly the research of asymptotic expressions in the theory of numbers was largely confined to the approximate determination of the summatory function (or the mean value) of a given arithmetic function. 2014 M. Overholt Course Anal. Number Theory i. 23 To calculate a local average by differencing an estimate for the associated summatory function is not always efficient. This entry has been updated (OED Third Edition, September 2019; most recently modified version published online March 2022). < adj.1704
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