If is equal to the sum of its Taylor series for all in the complex plane, it is called entire. The polynomials, exponential function , and the trigonometric functions sine and cosine, are examples of entire functions. Examples of functions that are not entire include the square root, the logarithm, the trigonometric function tangent, and its inverse, arctan. For these functions the Taylor series do not converge if is far from . That is, the Taylor series diverges at if the distance between and is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point.
If is equal to the sum of its Taylor series for all in the complex plane it is called entire. The polynomials, exponential function , and the trigonometric functions sine and cosine, are examples of entire functions. Examples of functions that are not entire include the square .root, the logarithm, the trigon,ometric function tangent, and its inverse, arctan. For these functions the Taylor series do not converge if is far from  That is, the Taylor series diverges at if the distance between and is larger than the radius of convergence. The Taylor series can be used to calculate the value of an entire function at every point, if the value of the function, and of all of its derivatives, are known at a single point.