# Even part

From Calculus

## Definition

Suppose is a function whose domain is a subset of the reals that is symmetric about 0, i.e., for every in the domain of , is also in the domain of . Then, the **even part** of , sometimes denoted or is defined as a function with the same domain, and with the definition:

Equivalently, it is the only possible choice of even function in a decomposition of of the form:

with both having the same domain as , and with an even function and an odd function. The other part, , is the odd part of .

## Particular cases

Function | Domain | Even part |
---|---|---|

polynomial | all of | the sum of the monomials of even degree in that polynomial |

exponential function | all of | hyperbolic cosine function |