odd function

odd function

[′äd ‚fəŋk·shən]
(mathematics)
A function ƒ(x) is odd if, for every x, ƒ(-x) = -ƒ(x).
References in classic literature ?
Indeed, except in respect of staring about him (a branch of the public service to which the pictorial cherub is much addicted), this domestic cherub discharged as many odd functions as his prototype; with the difference, say, that he performed with a blacking-brush on the family's boots, instead of performing on enormous wind instruments and double-basses, and that he conducted himself with cheerful alacrity to much useful purpose, instead of foreshortening himself in the air with the vaguest intentions.
where [alpha] and [beta] are positive constants; [a.sub.ij] is the (i, j) element of A and [phi](*) is an odd function.
That is f is an odd function. Interchanging x with y in (16), we see that
(a) Cross section of covariances [mathematical expression not reproducible] and [mathematical expression not reproducible] for even and odd function. Each covariance is similar to a sinc function centred at f = f', where a tip is added on top.
If [F.sub.1](x) = [F.sub.11]([x.sub.1]) + [F.sub.12]([x.sub.2], ..., [x.sub.n]) is an odd function or [F.sub.11] ([x.sub.1]) = [[alpha].sub.1][x.sub.1], then [E.sub.1] = [x.sub.1] + [y.sub.1] can be made, where [[alpha].sub.1] is a real number.
I have indicated to our President and CEO that if there is anything I can do in the future, just reach out, so with that in mind I hope I keep running into you all at the odd function.
The gossip function f(x) is an odd function; thus f([x.sub.j](n) - [x.sub.j](n)) + f([x.sub.i](n) - [x.sub.j](n)) = 0.
It is easy to realize that [i.sub.nl](0) = 0 and, due to the circuit symmetry, [i.sub.nl](v) is an odd function of v.
We can verify this by substituting (11) into (10) and by using the fact that S'p(x)is an odd function such as [S'.sub.p] (x) = - [S'.sub.p] (-x) since the derivative of the even function becomes an odd function [19].
On the other hand, the quadrature angles are the zeros of [p.sub.n+1] (x([theta])), where {[p.sub.k]}k[greater than or equal to]0 are the algebraic orthogonal polynomials with respect to the weight function (1.8); the functions {[p.sub.k] (x([theta]))} are indeed orthogonal in d[theta], but they are not all trigonometric polynomials, since [p.sub.k] is an odd function for k odd(cf.