# Zeros of Truncated Series of Elementary Functions

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

The radius of convergence of a series expansion of a function equals the distance from the expansion point to the nearest singularity of the function in the complex plane. This means that for entire functions, such as the exponential function, sine, and cosine, the radius of convergence of the series is infinite and the zeros of the truncated series approach the zeros of the function. This Demonstration shows the zeros of the truncated series of elementary functions. For functions with singularities in the finite part of the complex plane, such as tangent or cotangent, the zeros must cluster at the circle of convergence.

Contributed by: Michael Trott (April 2007)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

detailSectionParagraph## Permanent Citation

"Zeros of Truncated Series of Elementary Functions"

http://demonstrations.wolfram.com/ZerosOfTruncatedSeriesOfElementaryFunctions/

Wolfram Demonstrations Project

Published: April 27 2007