| 单词 | binomial expansion |
| 释义 | > as lemmasbinomial expansion 1. Mathematics. Consisting of two terms; see B. Also, relating to or derived from the binomial theorem or the binomial distribution; binomial coefficient: a coefficient of a term in a binomial expansion; binomial distribution: a frequency distribution of the possible number of successful outcomes in a given number of trials in each of which there is the same probability of success; binomial equation: an equation reducible to the form xn − A = 0; binomial expansion: an expansion of a power of a binomial; binomial series: an infinite series obtained by expanding (x + y)n, where n is not a positive integer or zero; also, a binomial expansion; binomial theorem: the general algebraic formula, discovered by Newton, by which any power of a binomial quantity may be found without performing the progressive multiplications. ΘΚΠ the world > relative properties > number > algebra > [adjective] > relating to expressions > involving specific number of terms binomial1570 multinomial1608 quadrinomial1673 solinomial1690 polynomial1704 trinomial1704 infinitinomial1706 monomial1801 tetranomial1817 unipartite1819 monome1829 mononomial1861 polynomic1868 tripartite1869 multinominal1940 the world > relative properties > number > algebra > [noun] > expression > formula binomial theorem1755 formula1794 Rankine's formula1868 proportionality1882 Hero's formula1886 Rutherford's law1913 Mellin transform1927 Langevin equation1943 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 the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms > method relating to Horner's method1842 binomial expansion1848 the world > relative properties > number > algebra > [noun] > expression > consisting of specific number of terms > method relating to > coefficient of binomial coefficient1889 the world > relative properties > number > probability or statistics > [noun] > distribution distribution1854 random distribution1882 frequency distribution1895 probability distribution1895 Poisson distribution1898 binomial distribution1911 Student's t-distribution1925 sampling distribution1928 probability density1931 Poisson1940 beta distribution1941 Cauchy distribution1948 geometric distribution1950 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 1570 H. Billingsley tr. Euclid Elements Geom. x. f. 258 If two rationall lines commensurable in power onely be added together: the whole line is irrationall, and is called a binomium, or a binomiall line. 1673 J. Kersey Elem. Algebra I. ii. i. 137 (heading) Production of Powers, from Roots Binomial, Trinomial, &c. 1706 Phillips's New World of Words (new ed.) (at cited word) A binomial Quantity or Root, i.e. a Quantity or Root that consists of two Names or Parts joyn'd together by the Sign + as a + b, or 3 + 2. 1755 J. Landen Math. Lucubrations ix. 132 By the Binomial Theorem p/ 1 + x is = 1 + px + p.p − 1/ 2x2 + p.p − 1. p − 2/ 2.3x3 &c. 1796 C. Hutton Math. & Philos. Dict. (new ed.) I. 208/2 He [sc. Newton] happily discovered that, by considering powers and roots in a continued series,..the same binomial series would serve for them all, whether the index should be fractional or integral. 1814 P. Barlow New Math. & Philos. Dict. Binomial equation, is any equation of two terms, but more commonly applied to the higher order of equations of the form xn = 1. 1848 A. De Morgan in Cambr. & Dublin Math. Jrnl. III. 239 Use the binomial expansion up to the term in (x − b)−(n−1). 1870 F. C. Bowen Logic xii. 410 The Binomial Theorem..is a true Law of Nature according to our definition. 1889 Cent. Dict. Binomial coefficient. 1911 G. U. Yule Introd. Theory Statistics xv. 305 The binomial distribution,..only becomes approximately normal when n is large, and this limitation must be remembered in applying the table..to cases in which the distribution is strictly binomial. 1914 Biometrika 10 36 Binomial frequencies belong to the teetotum class of chances. 1925 R. A. Fisher Statist. Methods iii. 65 The binomial distribution is well known as the first example of a theoretical distribution to be established. 1948 J. V. Uspensky Theory Equations i. 26 The particular binomial equation xn = 1, defining the so-called roots of unity of degree n, is of special interest. 1949 W. L. Ferrar Higher Algebra Schools v. 73 The binomial expansion can be used to find the value of expressions such as (1·002)13, (1·01)7 to any desired number of significant figures. 1959 G. James & R. C. James Math. Dict. (ed. 2) 31/1 The (r + 1)th binomial coefficient of order n (n a positive integer) is n!/[r!(n − r)!], the number of combinations of n things r at a time. 1961 P. G. Guest Numerical Methods Curve Fitting iv. 72 The binomial distribution for rare events..approximates to the Poisson form. 1966 McGraw-Hill Encycl. Sci. & Technol. (rev. ed.) XII. 191/2 One of the most important power series is the binomial series. < as lemmas |
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