even and odd functions
Although this entry is mainly concerned with functions , the definition can be generalized to other types of function.
The function is odd.
The function is even.
The sine and cosine functions are odd and even, respectively.
The only function that is both even and odd is the function defined by for all real .
A sum of even functions is even, and a sum of odd functions is odd. In fact, the even functions form a real vector space, as do the odd functions.
Every real function can be expressed in a unique way as the sum of an odd function and an even function.
The Fourier transform of a real even function is purely real and even. The Fourier transform of a real odd function is purely imaginary and odd.
|Title||even and odd functions|
|Date of creation||2013-03-22 13:34:19|
|Last modified on||2013-03-22 13:34:19|
|Last modified by||yark (2760)|