Even and odd functions: Difference between revisions

Revision as of 13:30, 9 February 2005

Revision as of 00:40, 24 April 2005

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==Odd functions==

Again, let ''f''(''x'') be a [[real number|real]] valued function of a real variable. Then ''f'' is '''odd''' if the following equation holds for all real ''x'':

:''f''(−''x'') = −''f''(''x'')

Geometrically, an odd function is symmetric with respect to rotation about the [[origin]].

The designation '''odd''' is due to the fact that the Taylor series of an odd function includes only odd powers.