Taylor polynomial
Revision as of 16:29, 9 March 2022 by Orange quail 9 (talk | contribs) (Basic facts; will add details later.)
The degree- Taylor polynomial of a function
about
is the unique polynomial of degree
whose value and first
derivatives match the value and first
derivatives of
at
.
The formula for a degree- Taylor polynomial of
about
is
In the formula above,
denotes the order-
derivative of
.
Taylor polynomials are often used to approximate non-polynomial functions that cannot be calculated exactly, such as trigonometric functions, exponential functions, and logarithms.
Contents
Derivation of the formula
Special cases
Maclaurin polynomial
Tangent-line approximation
Error bound
Taylor series
The Taylor series of an infinitely differentiable function is the infinite series
The partial sums of this series are the Taylor polynomials of
of each degree.