Taylor series
Taylor series noun: 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.
Noun
Taylor series (plural Taylor series)
- 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.
- 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...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
- 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
Taylor series meaning in Tamil
Taylor series in Tamil
- டைலர் தொடர்
Examples of Taylor series in a sentence
- A series solution about an ordinary point of a differential equation is always a Taylor series having a nonvanishing radius of convergence.1978, [McGraw-Hill], Carl M. Bender, Steven A. Orszag, Advanced Mathematical Methods for Scientists and Engineers I: Asymptotic Methods and...
- 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:
Forms of Taylor series
| plural | Taylor series |
|---|---|
| alternative form | Taylor's series |
Origin of Taylor series
Named after English mathematician Brook Taylor, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician James Gregory.
Questions about Taylor series
- What does Taylor series mean?
- Taylor series means 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.
- What is Taylor series in Tamil?
- Taylor series in Tamil is டைலர் தொடர். See Taylor series meaning in Tamil.
- How do you use Taylor series in a sentence?
- A series solution about an ordinary point of a differential equation is always a Taylor series having a nonvanishing radius of convergence.
- What part of speech is Taylor series?
- Taylor series is a noun.
- What is the plural of Taylor series?
- The plural of Taylor series is Taylor series.
Words near Taylor series in the dictionary
Source and license
Adapted from Wiktionary: Taylor series (page history and authors); taylor series (Tamil Wiktionary) (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
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Cite this entry: “Taylor series.” Word.ws, https://word.ws/taylor_series. Based on Wiktionary, CC BY-SA 4.0.