Dictionary

Taylor series en · NOUN

Etymology

Named after English mathematician Brook Taylor, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician James Gregory.

Meanings

1. A power series representation of given infinitely differentiable function f whose terms are calculated from the function's arbitrary order derivatives at given reference point a; the series f(a)+(f'(a))/(1!)(x-a)+(f(a))/(2!)(x-a)²+(f'(a))/(3!)(x-a)³+⋯=∑ₙ₌₀∞(f⁽ⁿ⁾(a))/(n!)(x-a)ⁿ.
   • The usual procedure for deriving finite-difference equations consists of approximating the derivatives in the differential equation via a truncated Taylor series. 1980, Suhas Patankar, Numerical Heat Transfer and Fluid Flow, Taylor & Francis (CRC Press), page 28:
   • This function has its only singularity at x = 0, implying that the radius of convergence for the Taylor series around x = 1 is only unity. 1998, Kenneth L. Judd, Numerical Methods in Economics, The MIT Press, page 197:
   • A series solution about an ordinary point of a differential equation is always a Taylor series having a nonvanishing radius of convergence. A series solution about a singular point does not have this form (except in rare cases). Instead, it may be either a convergent series not in Taylor series form (such as a Frobenius series) or it may be a divergent series. 1978, [McGraw-Hill], Carl M. Bender, Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and Perturbation Theory, Springer, published 1999, page 324:

Forms

Hyponyms

Maclaurin series (power series of a function calculated from derivatives at a reference point)

Translations (18)

hu Taylor-sor (power series of a function calculated from derivatives at a reference point) · de Taylorreihe (power series of a function calculated from derivatives at a reference point) · fi Taylorin sarja (power series of a function calculated from derivatives at a reference point) · cs Taylorova řada (power series of a function calculated from derivatives at a reference point) · da Taylorrække (power series of a function calculated from derivatives at a reference point) · cmn 泰勒展開式 /泰勒展开式 (power series of a function calculated from derivatives at a reference point) · pt série de Taylor (power series of a function calculated from derivatives at a reference point) · ast serie de Taylor (power series of a function calculated from derivatives at a reference point) · pl szereg Taylora (power series of a function calculated from derivatives at a reference point) · bg Тейлъров ред (power series of a function calculated from derivatives at a reference point) · it serie di Taylor (power series of a function calculated from derivatives at a reference point) · bg ред на Тейлър (power series of a function calculated from derivatives at a reference point) · fr série de Taylor (power series of a function calculated from derivatives at a reference point) · es serie de Taylor (power series of a function calculated from derivatives at a reference point) · ru ряд Те́йлора (power series of a function calculated from derivatives at a reference point) · ca sèrie de Taylor (power series of a function calculated from derivatives at a reference point) · ro serie Taylor (power series of a function calculated from derivatives at a reference point) · gl serie de Taylor (power series of a function calculated from derivatives at a reference point)

wikipedia: James Gregory (mathematician) · wikipedia: Brook Taylor