taylor series
Word Rarity
Uncommon
Frequency: Zipf frequency 4.57 in modern English
15
Scrabble Score
12
Letters
2
Syllables
9
Unique Chars
Meaning
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.
Example Sentences
- "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."
- "The usual procedure for deriving finite-difference equations consists of approximating the derivatives in the differential equation via a truncated Taylor series."
- "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."
Etymology
Named after English mathematician Brook Taylor, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician James Gregory.