Maclaurinn.

Brit.

/məˈklɒrɪn/, U.S.

/məˈklɔrɪn/

Origin: From a proper name. Etymon: proper name Maclaurin.

Etymology: < the name of Colin Maclaurin (1698–1746), Scottish mathematician, who first described the series.

Mathematics.

1. Maclaurin's theorem n. Taylor's theorem applied to a function at the origin.

ΘΚΠ

the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem > relating to functions

Taylor's theorem1816

Maclaurin's theorem1820

Leibniz theorem1852

Green's theorem1857

Laurent's theorem1893

factor theorem1894

factor law1901

1820 G. Peacock Coll. Examples Differential & Integral Calculus i. 41 Examples given by our author of the application of Maclaurin's theorem to the developement of transcendental functions.

1934 E. J. McShane tr. R. Courant Differential & Integral Calculus I. vi. 320 A special case of this [sc. Taylor's] theorem is often referred to..as Maclaurin's theorem.

1972 M. Kline Math. Thought xx. 442 Taylor's theorem for a = 0 is now called Maclaurin's theorem.

2. Maclaurin's series n. (also Maclaurin series) [described in Maclaurin Treat. Fluxions (1742) ii. ii. 610] a Taylor series representing a function in the neighbourhood of the origin.

ΘΚΠ

the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > series > infinite

secundan1685

infinite series1706

Taylor('s) series1816

Maclaurin's series1881

power series1884

Fibonacci('s) series1891

Laurent's expansion1893

Fibonacci('s) numbers1914

majorant1925

tetrahedral numbers1939

Fibonacci('s) sequence1964

binomial series1966

1881 Encycl. Brit. XIII. 19/2 The result is usually called Maclaurin's series, having been given in his Fluxions (1742). It had, however, been previously published by Stirling in his Meth. Diff. (1717); but neither Stirling nor Maclaurin laid any claim to the theorem as being original, both referring it to Taylor.

1902 J. W. Mellor Higher Math. v. 227 The series on the right-hand side is known as Maclaurin's Series.

1970 Amer. Jrnl. Physics 38 1293/1 A series in positive integral powers of t—namely, a Taylor (or Maclaurin) series.

1989 Numerische Math. 55 281 For the function arctan z, we give graphical contour maps of the number of significant digits in the approximations f_n(z), g_n(z) and p_n(z), the nth partial sum of the Maclaurin series, for z in a key region of the complex plane.

This entry has been updated (OED Third Edition, March 2000; most recently modified version published online March 2022).

单词	maclaurin
释义	Maclaurinn. Brit. /məˈklɒrɪn/, U.S. /məˈklɔrɪn/ Origin: From a proper name. Etymon: proper name Maclaurin. Etymology: < the name of Colin Maclaurin (1698–1746), Scottish mathematician, who first described the series. Mathematics. 1. Maclaurin's theorem n. Taylor's theorem applied to a function at the origin. ΘΚΠ the world > relative properties > number > mathematics > [noun] > mathematical enquiry > proposition > theorem > specific theorem > relating to functions Taylor's theorem1816 Maclaurin's theorem1820 Leibniz theorem1852 Green's theorem1857 Laurent's theorem1893 factor theorem1894 factor law1901 1820 G. Peacock Coll. Examples Differential & Integral Calculus i. 41 Examples given by our author of the application of Maclaurin's theorem to the developement of transcendental functions. 1934 E. J. McShane tr. R. Courant Differential & Integral Calculus I. vi. 320 A special case of this [sc. Taylor's] theorem is often referred to..as Maclaurin's theorem. 1972 M. Kline Math. Thought xx. 442 Taylor's theorem for a = 0 is now called Maclaurin's theorem. 2. Maclaurin's series n. (also Maclaurin series) [described in Maclaurin Treat. Fluxions (1742) ii. ii. 610] a Taylor series representing a function in the neighbourhood of the origin. ΘΚΠ the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > series > infinite secundan1685 infinite series1706 Taylor('s) series1816 Maclaurin's series1881 power series1884 Fibonacci('s) series1891 Laurent's expansion1893 Fibonacci('s) numbers1914 majorant1925 tetrahedral numbers1939 Fibonacci('s) sequence1964 binomial series1966 1881 Encycl. Brit. XIII. 19/2 The result is usually called Maclaurin's series, having been given in his Fluxions (1742). It had, however, been previously published by Stirling in his Meth. Diff. (1717); but neither Stirling nor Maclaurin laid any claim to the theorem as being original, both referring it to Taylor. 1902 J. W. Mellor Higher Math. v. 227 The series on the right-hand side is known as Maclaurin's Series. 1970 Amer. Jrnl. Physics 38 1293/1 A series in positive integral powers of t—namely, a Taylor (or Maclaurin) series. 1989 Numerische Math. 55 281 For the function arctan z, we give graphical contour maps of the number of significant digits in the approximations f_n(z), g_n(z) and p_n(z), the nth partial sum of the Maclaurin series, for z in a key region of the complex plane. This entry has been updated (OED Third Edition, March 2000; most recently modified version published online March 2022). < n.1820
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