Pronunciation: ' t ā -l ə r-
Function: noun
Etymology: Brook Taylor † 1731 English mathematician
Date: 1842
: 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 f ( x ) = f ( a ) + ( f [ 1 ] ( a )/1!)( x - a ) + ( f [ 2 ] ( a )/2!)( x - a ) 2 + ⋯ + ( f [ n ] ( a )/ n !)( x - a n + ⋯ where f [ n ] ( a ) is the derivative of nth order of f ( x ) evaluated at a ― called also Taylor's series