recursionn.

Brit.

/rᵻˈkəːʃn/,

/rᵻˈkəːʒn/, U.S.

/rəˈkərʒ(ə)n/

Origin: A borrowing from Latin. Etymons: Latin recursion-, recursio.

Etymology: < post-classical Latin recursion-, recursio return, recurrence (5th cent.) < classical Latin recurs- , past participial stem of recurrere recur v. + -iō -ion suffix¹. Compare recurrency n.

1. The action or an act of recurring or returning. Now rare.

ΘΚΠ

the world > movement > motion in a certain direction > backward movement > [noun] > return towards point of departure

returna1393

returning?c1400

recoursec1405

regress1478

reverture1495

retraira1500

regression1598

reflexa1613

recursion1616

revolture1633

retroition1651

hark back1798

recover1818

1616 J. Bullokar Eng. Expositor Recursion, a running backe.

1660 R. Boyle New Exper. Physico-mechanicall xxvi. 203 The Recursions of that Pendulum which was swinging within the Receiver.

1677 R. Gilpin Dæmonol. Sacra ii. vii. 307 Our Passions, in their workings, do depend upon the fluctuations, excursions and recursions of the Blood, and animal Spirits.

1720–21 Lett. from Mist's Jrnl. (1722) II. 33 The present melancholy Prospect of the Recursion of the South-Sea Tide.

1792 H. H. Brackenridge Mod. Chivalry I. ii. ii. 54 Volunteers are the thing, making a sudden incursion. If they make a sudden incursion, they will make a sudden recursion, and leave the matter as they found it.

1830 T. Taylor tr. Celsus Arguments 23 The doctrine..that in long periods of time, recursions and concursions of the stars, conflagrations and deluges take place.

2001 P. D. Fenves Arresting Lang. v. 161 The same signature appears at the end of an anecdote than can be understood as the revision of ‘The Marquise von O...’—or as the recursion of the story to its original status as anecdote.

2. Mathematics, Computing, and Linguistics.

a. The application, use, or occurrence of a recursive procedure, definition, subroutine, etc.primitive recursion: see the first element.

ΘΚΠ

the world > relative properties > number > mathematics > [noun] > mathematical enquiry > process of calculating > use of repeated procedure

recursion1895

iteration1924

1895 Ann. Math. 9 35 The readiest method of accomplishing this is to proceed by successive approximations using formulas of recursion.

1914 Amer. Math. Monthly 21 165 The theorem so obtained would afford a means of recursion by which a sequence of indefinitely increasing prime numbers could be written out consecutively. No such tool has yet been invented.

1961 Communications ACM 4 65/1 The growing extent and direction of application of recursion in programming research.

1964 E. Bach Introd. Transformational Gram. iii. 46 Care must be taken to ensure that unwanted recursion (looping) does not occur.

1975 F. R. Palmer in W. F. Bolton Eng. Lang. i. 34 The structure of language involves ‘recursion’ of the kind illustrated by ‘This is the house that Jack built’, ‘This is the mouse that lived in the house that Jack built’ and so on—if necessary ad infinitum.

2004 M. Potter Set Theory & its Philos. v. 93 The sequence (x_n) is said to be defined by recursion from the equation x₀ = a, x_{n + 1} = f(x_n).

b. An instance of this; a recursive definition; (Computing) a recursive statement, subroutine, etc.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > function > property of

discontinuity1803

functionality1857

self-conjugation1866

covariance1878

symmetry1888

monogeneity1906

recursion1913

recursive definition1935

holomorphy1957

unateness1960

1913 Amer. Math. Monthly 20 220 Starting from (17) we should be led to an equation..where σ₂ > σ₁; and so on indefinitely. But such a recursion is impossible.

1930 Trans. Amer. Math. Soc. 32 908 The above t_v are not mutually independent but are connected by algebraic recursions.

1963 W. V. Quine Set Theory §11. 79 There are the familiar so-called recursive definitions or recursions.

1966 N. Chomsky Topics Theory Generative Gram. ii. 33 An utterly fantastic proposal, namely, that a grammar should contain no recursions in its system of rules.

1971 Computers & Humanities 5 155 algol is more powerful in that it allows recursions, has block structure, and permits expressions in many places.

2006 Appl. Math. & Computation 179 147 (title) The recursions of order conditions for some Runge–Kutta-like methods.

Compounds

recursion formula n. [after German Recursionsformel (1871 or earlier; now Rekursionsformel)] Mathematics an equation relating the value of a function for given values of its arguments to its values for other values of the arguments.

ΘΚΠ

the world > relative properties > number > algebra > [noun] > expression > equation

equation1570

cardanic equation1684

binomial equation1814

simultaneous equation1816

characteristic equation1828

characteristic equation1841

characteristic equation1849

intrinsic equation of a curve1849

complete primitive1859

primitive1862

Poisson's equation1873

Jacobi equation1882

formulaic equation1884

adjoint1889

recursion formula1895

characteristic equation1899

characteristic equation1900

Pell equation1910

Lotka–Volterra equations1937

Langevin equation1943

1895 Ann. Math. 9 46 This recursion formula..leads to the following determination of the c's with even suffixes.

1996 C. Goureriéoux & A. Monfort Simulation-Based Econometric Methods v. 105 It is a simple exercise to establish the following recursion formula: Ψ(t, μ, 0) = Φ(t), Ψ(t, μ, r) = (r − 1)Ψ(t, μ, r − 2) − μΨ (t, μ, r − 1) − (t − μ)^{r −1}φ(t).

This entry has been updated (OED Third Edition, June 2009; most recently modified version published online March 2022).

单词	recursion
释义	recursionn. Brit. /rᵻˈkəːʃn/, /rᵻˈkəːʒn/, U.S. /rəˈkərʒ(ə)n/ Origin: A borrowing from Latin. Etymons: Latin recursion-, recursio. Etymology: < post-classical Latin recursion-, recursio return, recurrence (5th cent.) < classical Latin recurs- , past participial stem of recurrere recur v. + -iō -ion suffix¹. Compare recurrency n. 1. The action or an act of recurring or returning. Now rare. ΘΚΠ the world > movement > motion in a certain direction > backward movement > [noun] > return towards point of departure returna1393 returning?c1400 recoursec1405 regress1478 reverture1495 retraira1500 regression1598 reflexa1613 recursion1616 revolture1633 retroition1651 hark back1798 recover1818 1616 J. Bullokar Eng. Expositor Recursion, a running backe. 1660 R. Boyle New Exper. Physico-mechanicall xxvi. 203 The Recursions of that Pendulum which was swinging within the Receiver. 1677 R. Gilpin Dæmonol. Sacra ii. vii. 307 Our Passions, in their workings, do depend upon the fluctuations, excursions and recursions of the Blood, and animal Spirits. 1720–21 Lett. from Mist's Jrnl. (1722) II. 33 The present melancholy Prospect of the Recursion of the South-Sea Tide. 1792 H. H. Brackenridge Mod. Chivalry I. ii. ii. 54 Volunteers are the thing, making a sudden incursion. If they make a sudden incursion, they will make a sudden recursion, and leave the matter as they found it. 1830 T. Taylor tr. Celsus Arguments 23 The doctrine..that in long periods of time, recursions and concursions of the stars, conflagrations and deluges take place. 2001 P. D. Fenves Arresting Lang. v. 161 The same signature appears at the end of an anecdote than can be understood as the revision of ‘The Marquise von O...’—or as the recursion of the story to its original status as anecdote. 2. Mathematics, Computing, and Linguistics. a. The application, use, or occurrence of a recursive procedure, definition, subroutine, etc.primitive recursion: see the first element. ΘΚΠ the world > relative properties > number > mathematics > [noun] > mathematical enquiry > process of calculating > use of repeated procedure recursion1895 iteration1924 1895 Ann. Math. 9 35 The readiest method of accomplishing this is to proceed by successive approximations using formulas of recursion. 1914 Amer. Math. Monthly 21 165 The theorem so obtained would afford a means of recursion by which a sequence of indefinitely increasing prime numbers could be written out consecutively. No such tool has yet been invented. 1961 Communications ACM 4 65/1 The growing extent and direction of application of recursion in programming research. 1964 E. Bach Introd. Transformational Gram. iii. 46 Care must be taken to ensure that unwanted recursion (looping) does not occur. 1975 F. R. Palmer in W. F. Bolton Eng. Lang. i. 34 The structure of language involves ‘recursion’ of the kind illustrated by ‘This is the house that Jack built’, ‘This is the mouse that lived in the house that Jack built’ and so on—if necessary ad infinitum. 2004 M. Potter Set Theory & its Philos. v. 93 The sequence (x_n) is said to be defined by recursion from the equation x₀ = a, x_{n + 1} = f(x_n). b. An instance of this; a recursive definition; (Computing) a recursive statement, subroutine, etc. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > function > property of discontinuity1803 functionality1857 self-conjugation1866 covariance1878 symmetry1888 monogeneity1906 recursion1913 recursive definition1935 holomorphy1957 unateness1960 1913 Amer. Math. Monthly 20 220 Starting from (17) we should be led to an equation..where σ₂ > σ₁; and so on indefinitely. But such a recursion is impossible. 1930 Trans. Amer. Math. Soc. 32 908 The above t_v are not mutually independent but are connected by algebraic recursions. 1963 W. V. Quine Set Theory §11. 79 There are the familiar so-called recursive definitions or recursions. 1966 N. Chomsky Topics Theory Generative Gram. ii. 33 An utterly fantastic proposal, namely, that a grammar should contain no recursions in its system of rules. 1971 Computers & Humanities 5 155 algol is more powerful in that it allows recursions, has block structure, and permits expressions in many places. 2006 Appl. Math. & Computation 179 147 (title) The recursions of order conditions for some Runge–Kutta-like methods. Compounds recursion formula n. [after German Recursionsformel (1871 or earlier; now Rekursionsformel)] Mathematics an equation relating the value of a function for given values of its arguments to its values for other values of the arguments. ΘΚΠ the world > relative properties > number > algebra > [noun] > expression > equation equation1570 cardanic equation1684 binomial equation1814 simultaneous equation1816 characteristic equation1828 characteristic equation1841 characteristic equation1849 intrinsic equation of a curve1849 complete primitive1859 primitive1862 Poisson's equation1873 Jacobi equation1882 formulaic equation1884 adjoint1889 recursion formula1895 characteristic equation1899 characteristic equation1900 Pell equation1910 Lotka–Volterra equations1937 Langevin equation1943 1895 Ann. Math. 9 46 This recursion formula..leads to the following determination of the c's with even suffixes. 1996 C. Goureriéoux & A. Monfort Simulation-Based Econometric Methods v. 105 It is a simple exercise to establish the following recursion formula: Ψ(t, μ, 0) = Φ(t), Ψ(t, μ, r) = (r − 1)Ψ(t, μ, r − 2) − μΨ (t, μ, r − 1) − (t − μ)^{r −1}φ(t). This entry has been updated (OED Third Edition, June 2009; most recently modified version published online March 2022). < n.1616
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