| 单词 | taylor's theorem |
| 释义 | > as lemmasTaylor's theorem 1. Mathematics. Taylor('s) series, an infinite series of the form f(a) + hf′(a) + h2f″(a)/2! + … + hn−1f(n−1)(a)/(n − 1)! + …, where f(i)(a) is the value of the ith derivative of a function f(x) at x = a; an analogous series for a function of more than one variable; Taylor's theorem, the theorem that a function f(x) can be approximated over any interval throughout which its first n derivatives exist by the first n terms of Taylor's series (with h = x − a) plus a remainder dependent on f(n)(a + θh) (0 < θ < 1). 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 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 1816 tr. S. F. Lacroix Elem. Treat. Differential & Integral Calculus 22 This formula is called Taylor's Theorem, from the English geometer by whom it was discovered. 1842 Penny Cycl. XXIV. 126/2 Lagrange's paper in the Berlin Memoirs for 1772, in which he proposed to make Taylor's theorem the foundation of the Differential Calculus. 1842 Penny Cycl. XXIV. 126/2 D'Alembert..gave for the first time..a method of finding the remnant of Taylor's series after a certain number of terms have been taken. 1908 G. H. Hardy Course Pure Math. vii. 255 This expansion of f(a + h) is known as Taylor's series. 1908 G. H. Hardy Course Pure Math. vii. 287 (heading) Proof of Taylor's theorem by integration of parts. 1968 C. G. Kuper Introd. Theory Superconductivity ii. 24 Near the transition temperature, g may be expanded in a Taylor series: g = g0 + αζ + ½βζ2 + … 1972 A. W. F. Edwards Likelihood v. 72 An alternative method, which readily generalizes to the case of many parameters, is to obtain the Taylor's series approximation to the support curve in the region of the maximum. 1972 M. Kline Math. Thought xx. 442 Taylor's theorem for a = 0 is now called Maclaurin's theorem. 1979 E. S. Page & L. B. Wilson Introd. Computational Combinatorics ii. 10 We write E = 1 + ∆ and expand the polynomial f by Taylor's theorem. < as lemmas |
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