Difference between revisions of "Even part"
(Created page with "==Definition== Suppose <math>f</math> is a function whose domain is a subset of the reals that is symmetric about 0, i.e., for every <math>x</math> in the domain of <math>f</mat...")
Revision as of 12:42, 28 August 2011
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:
|polynomial||all of||the sum of the monomials of even degree in that polynomial|
|exponential function||all of||hyperbolic cosine function|