“Taylor series”的概念、定义、翻译、参考文献-科学参考

Taylor series

Physics

The infinite power series of derivatives into which a function f(x) can be expanded, for a fixed value of the variable x=a:

$f (x) = f (a) + f' (a) (x - a) + f ″ (a) {(x - a)}^{2} / 2! + …$

When a=0, the series formed is known as Maclaurin’s series:

$f (x) = f (0) + f' (0) x + f ″ (0) x^{2} / 2! + …$

The series was discovered by Brook Taylor (1685–1731) and the special case was named after Colin Maclaurin (1698–1746).

Mathematics

See Taylor’s Theorem.

Chemical Engineering

An infinite power series used to determine the development of a given function. Obtained from Taylor’s theorem, a function f(x) can be expanded to the nth degree as:
$f (x) = f (a) + \frac{f^{'} (a)}{1!} (a - x) + \frac{f^{″} (a)}{2!} {(x - a)}^{2} + \dots$

Taylor’s formula gives f(x) with increasing accuracy, the larger the series used. The Taylor series can be used to develop a given function f(x) in powers of (x−a). It was developed by Brook Taylor (1685–1731).

单词	Taylor series
释义	Taylor series Physics The infinite power series of derivatives into which a function f(x) can be expanded, for a fixed value of the variable x=a: $f (x) = f (a) + f' (a) (x - a) + f ″ (a) {(x - a)}^{2} / 2! + …$ When a=0, the series formed is known as Maclaurin’s series: $f (x) = f (0) + f' (0) x + f ″ (0) x^{2} / 2! + …$ The series was discovered by Brook Taylor (1685–1731) and the special case was named after Colin Maclaurin (1698–1746). Mathematics See Taylor’s Theorem. Chemical Engineering An infinite power series used to determine the development of a given function. Obtained from Taylor’s theorem, a function f(x) can be expanded to the nth degree as: $f (x) = f (a) + \frac{f^{'} (a)}{1!} (a - x) + \frac{f^{″} (a)}{2!} {(x - a)}^{2} + \dots$ Taylor’s formula gives f(x) with increasing accuracy, the larger the series used. The Taylor series can be used to develop a given function f(x) in powers of (x−a). It was developed by Brook Taylor (1685–1731).
随便看	Couette flow Couette rheometer cougar coulomb Coulomb barrier Coulomb blockade Coulomb, Charles Augustin de Coulomb, Charles Augustin de (1736–1806) Coulomb drag Coulomb explosion Coulomb failure criterion Coulomb field Coulomb force coulombmeter coulomb(symbol: C) Coulomb–Terzaghi shear strength equation Coulomb’s law Coulson, John Metcalfe (1910–90) coulter counter coulée flow coumarin coumarone Council for Mutual Economic Assistance Council for the Central Laboratory of the Research Councils council housing