The story
Named after English mathematician Brook Taylor, who formally introduced the series in 1715. The concept was formulated by Scottish mathematician James Gregory.
Etymology from Wiktionary, CC BY-SA 4.0.
Taylor series
Today it 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. Full definition →