majorantn.adj.

Brit.

/ˈmeɪdʒər(ə)nt/, U.S.

/ˈmeɪdʒərənt/

Origin: Formed within English, by derivation. Etymons: major adj., -ant suffix¹.

Etymology: < major adj. + -ant suffix¹. Compare earlier dominant adj. 2.

Mathematics.

A. n.

A function, set element, etc., that can be said to dominate, have precedence over, or constitute an upper bound for another mathematical entity of the same type, according to a particular criterion; spec. (a) a function whose absolute value for any value of the argument is not less than the corresponding absolute value of a given function; (b) a power series for which the absolute value of each term is not less than the absolute value of the corresponding term of a given power series (used esp. in ascertaining the convergence of the given series); (c) an element of an ordered set that is greater than or equal to every element of a given subset. Cf. dominant adj. 2.

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

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

numberc1350

extreme1571

numero1649

infinitesimal1655

No.1753

Z1842

majorant1925

seed1972

1925 Proc. London Math. Soc. 23 492 The inequality (a) is satisfied, not only by |B(z)|, but also by its majorant.

1942 Bull. Amer. Math. Soc. 48 925 This paper represents a different approach to a whole group of problems connected with majorants of subharmonic functions.

1979 Proc. London Math. Soc. 38 470 U has a non-negative harmonic majorant in D.

1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xxi. 481 If each function f_n(x) in the series F(x) = ∑∞n = 1f_n(x) is bounded, with |f_n(x)| ≤ M_n for all x in I, and if the series ∑∞n = 1M_n converges, then the series F(x) = ∑∞n = 1f_n(x) is uniformly convergent in the interval I. The series ∑∞n = 1M_n is then called a convergent majorant for ∑∞n = 1f_n(x).

1997 G. Nikolov (title) An inequality for polynomials with elliptic majorant.

B. adj.

Of the nature of a majorant. Also: of or relating to a majorant or majorants.

ΚΠ

1972 M. Kline Math. Thought xxvii. 639 Cauchy gives a powerful and easily applied criterion for the expansibility of a function in a Maclaurin series which uses a comparison series now called a majorant series.

1972 M. Kline Math. Thought xxviii. 701 Cauchy..called his method the calcul des limites but it is known today as the method of majorant functions.

1980 A. J. Jones Game Theory i. 39 In terms of pure strategies, the game has a minorant value −2 (A's gain floor) and a majorant value 2 (B's loss ceiling).

1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xxi. 481 The series ∑∞n = 1sin(nx)/n² is uniformly convergent for all x, because |sin(nx)/n²| ≤ 1/n² for all x and the majorant series ∑∞n = 11/n² converges.

1997 I. Grattan-Guinness Fontana Hist. Math. Sci. xiv. 586 The whole subject became extraordinarily difficult, requiring majorant arguments using upper bounding values in inequalities.

This is a new entry (OED Third Edition, June 2000; most recently modified version published online March 2022).

单词	majorant
释义	majorantn.adj. Brit. /ˈmeɪdʒər(ə)nt/, U.S. /ˈmeɪdʒərənt/ Origin: Formed within English, by derivation. Etymons: major adj., -ant suffix¹. Etymology: < major adj. + -ant suffix¹. Compare earlier dominant adj. 2. Mathematics. A. n. A function, set element, etc., that can be said to dominate, have precedence over, or constitute an upper bound for another mathematical entity of the same type, according to a particular criterion; spec. (a) a function whose absolute value for any value of the argument is not less than the corresponding absolute value of a given function; (b) a power series for which the absolute value of each term is not less than the absolute value of the corresponding term of a given power series (used esp. in ascertaining the convergence of the given series); (c) an element of an ordered set that is greater than or equal to every element of a given subset. Cf. dominant adj. 2. 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 the world > relative properties > number > mathematical number or quantity > numerical arrangement > [noun] > set > sequence > series > designating place in numberc1350 extreme1571 numero1649 infinitesimal1655 No.1753 Z1842 majorant1925 seed1972 1925 Proc. London Math. Soc. 23 492 The inequality (a) is satisfied, not only by \|B(z)\|, but also by its majorant. 1942 Bull. Amer. Math. Soc. 48 925 This paper represents a different approach to a whole group of problems connected with majorants of subharmonic functions. 1979 Proc. London Math. Soc. 38 470 U has a non-negative harmonic majorant in D. 1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xxi. 481 If each function f_n(x) in the series F(x) = ∑∞n = 1f_n(x) is bounded, with \|f_n(x)\| ≤ M_n for all x in I, and if the series ∑∞n = 1M_n converges, then the series F(x) = ∑∞n = 1f_n(x) is uniformly convergent in the interval I. The series ∑∞n = 1M_n is then called a convergent majorant for ∑∞n = 1f_n(x). 1997 G. Nikolov (title) An inequality for polynomials with elliptic majorant. B. adj. Of the nature of a majorant. Also: of or relating to a majorant or majorants. ΚΠ 1972 M. Kline Math. Thought xxvii. 639 Cauchy gives a powerful and easily applied criterion for the expansibility of a function in a Maclaurin series which uses a comparison series now called a majorant series. 1972 M. Kline Math. Thought xxviii. 701 Cauchy..called his method the calcul des limites but it is known today as the method of majorant functions. 1980 A. J. Jones Game Theory i. 39 In terms of pure strategies, the game has a minorant value −2 (A's gain floor) and a majorant value 2 (B's loss ceiling). 1989 W. Gellert et al. VNR Conc. Encycl. Math. (ed. 2) xxi. 481 The series ∑∞n = 1sin(nx)/n² is uniformly convergent for all x, because \|sin(nx)/n²\| ≤ 1/n² for all x and the majorant series ∑∞n = 11/n² converges. 1997 I. Grattan-Guinness Fontana Hist. Math. Sci. xiv. 586 The whole subject became extraordinarily difficult, requiring majorant arguments using upper bounding values in inequalities. This is a new entry (OED Third Edition, June 2000; most recently modified version published online March 2022). < n.adj.1925
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