Even and odd functions: Difference between revisions

Revision as of 15:38, 12 April 2004

Revision as of 15:45, 12 April 2004

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

Examples of even functions are: <math>x^2</math> and <math>cos(x)</math>

*x⁽²ⁿ⁾ where n is any non-negative integer

*The double [[derivative]] of any even function is an even function.

*<math>\cos(x)</math>

*The [[multiplication|product]] of 2 even functions is an even function.

*<math>\cosh(x)</math>

*The [[addition|sum]] of 2 even functions is an even function.

*The [[absolute value]]

*The double [[derivative]] of any even function

*The [[function composition|composition]] of any 2 functions, at least one of which is even

*The [[multiplication|product]] of 2 even functions

*The [[addition|sum]] of 2 even functions

==Odd functions==

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

Examples of odd functions are <math>x^3</math> and <math>\sin (x)</math>

==See also==