: a power series that gives the expansion of a function f (x) in the neighborhood of a point a provided that in the neighborhood the function is continuous, all its derivatives exist, and the series converges to the function in which case it has the form {latex}f(x) = f(a) + \frac{f'(a)}{1!}(x - a) + \frac{f''(a)}{2!}(x - a)^{2} + \dots + \frac{f^{[n]}(a)}{n!}(x - a)^{n}{/latex} where f[n] (a) is the derivative of nth order of f(x) evaluated at a
called also Taylor's series
Examples of Taylor series in a Sentence
Recent Examples on the Web
Intrigued by the anomaly, Martin dug into the game's source code and discovered that the landing algorithm was based on highly sophisticated physics for its time, including the Tsiolkovsky rocket equation and a Taylor series expansion.
—
Benj Edwards, Ars Technica, 14 June 2024
The latter is a general process known as a Taylor series expansion, which, in the case of the sine function, gives the polynomials discussed above.
—Quanta Magazine, 1 June 2022
Examples are automatically compiled from online sources to
show current usage.
Read More
Opinions expressed in the examples do not represent those of Merriam-Webster or its editors.
Send us feedback.
Benj Edwards, Ars Technica, 14 June 2024
The latter is a general process known as a Taylor series expansion, which, in the case of the sine function, gives the polynomials discussed above.
—Quanta Magazine, 1 June 2022
Dictionary Entries Near Taylor series
Cite this Entry
“Taylor series.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/Taylor%20series. Accessed 22 Nov. 2024.
Copy CitationLove words? Need even more definitions?
Merriam-Webster unabridged
Share