Meanings
alternative Taylor's series
- calculusA 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.
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 1972 more examples
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 324The 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
Synonyms & antonyms
Origin
Named after English mathematician Brook Taylor, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician James Gregory.
Full word history & related roots →Translations
Bulgarian ред на Тейлър, Тейлъров ред
- ред на Тейлър (red na Tejlăr)power series of a function calculated from derivatives at a reference point
- Тейлъров ред (Tejlărov red)power series of a function calculated from derivatives at a reference point
Catalan sèrie de Taylor
- sèrie de Taylorpower series of a function calculated from derivatives at a reference point
Chinese Mandarin 泰勒展開式 /泰勒展开式
- 泰勒展開式 /泰勒展开式 (Tàilè zhǎnkāishì)power series of a function calculated from derivatives at a reference point
Czech Taylorova řada
- Taylorova řadapower series of a function calculated from derivatives at a reference point
Danish Taylorrække
- Taylorrækkepower series of a function calculated from derivatives at a reference point
Finnish Taylorin sarja
- Taylorin sarjapower series of a function calculated from derivatives at a reference point
French série de Taylor
- série de Taylorpower series of a function calculated from derivatives at a reference point
German Taylorreihe
- Taylorreihepower series of a function calculated from derivatives at a reference point
Hungarian Taylor-sor
- Taylor-sorpower series of a function calculated from derivatives at a reference point
Italian serie di Taylor
- serie di Taylorpower series of a function calculated from derivatives at a reference point
Polish szereg Taylora
- szereg Taylorapower series of a function calculated from derivatives at a reference point
Portuguese série de Taylor
- série de Taylorpower series of a function calculated from derivatives at a reference point
Romanian serie Taylor
- serie Taylorpower series of a function calculated from derivatives at a reference point
Russian ряд Те́йлора
- ряд Те́йлора (rjad Tɛ́jlora)power series of a function calculated from derivatives at a reference point
Spanish serie de Taylor
- serie de Taylorpower series of a function calculated from derivatives at a reference point
Cite this entry
Taylor series. (n.d.). In WatkinsX Dictionary. Retrieved November 4, 2026, from https://dictionary.watkinsx.com/word/Taylor%20series
“Taylor series.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Taylor%20series. Accessed November 4, 2026.
WatkinsX Dictionary, s.v. “Taylor series,” accessed November 4, 2026, https://dictionary.watkinsx.com/word/Taylor%20series.
Source: Taylor series on Wiktionary, CC BY-SA 4.0.