Even And Odd Functions
In mathematics, even functions and odd functions are functions which satisfy particular symmetry relations, with respect to taking additive inverses. They are important in many areas of mathematical analysis, especially the theory of power series and Fourier series. They are named for the parity of the powers of the power functions which satisfy each condition: the function f(x) = xn is an even function if n is an even integer, and it is an odd function if n is an odd integer.
Read more about Even And Odd Functions: Definition and Examples, Some Facts, Harmonics
Famous quotes containing the words odd and/or functions:
“We have dancing ... from soon after sundown until a few minutes after nine o’clock.... Occasionally the boys who play the female partners in the dances exercise their ingenuity in dressing to look as girlish as possible. In the absence of lady duds they use leaves, and the leaf-clad beauties often look very pretty and always odd enough.”
—Rutherford Birchard Hayes (1822–1893)
“Nobody is so constituted as to be able to live everywhere and anywhere; and he who has great duties to perform, which lay claim to all his strength, has, in this respect, a very limited choice. The influence of climate upon the bodily functions ... extends so far, that a blunder in the choice of locality and climate is able not only to alienate a man from his actual duty, but also to withhold it from him altogether, so that he never even comes face to face with it.”
—Friedrich Nietzsche (1844–1900)