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A function f(x) satisfies the Lipschitz condition of order beta at x=0 if |f(h)-f(0)|<=B|h|^beta for all |h|<epsilon, where B and beta are independent of h, beta>0, and alpha ...

A function f such that |f(x)-f(y)|<=C|x-y| for all x and y, where C is a constant independent of x and y, is called a Lipschitz function. For example, any function with a ...

int_0^inftye^(-ax)J_0(bx)dx=1/(sqrt(a^2+b^2)), where J_0(z) is the zeroth order Bessel function of the first kind.

Li's criterion states that the Riemann hypothesis is equivalent to the statement that, for lambda_n=1/((n-1)!)(d^n)/(ds^n)[s^(n-1)lnxi(s)]|_(s=1), (1) where xi(s) is the ...

Lissajous curves are the family of curves described by the parametric equations x(t) = Acos(omega_xt-delta_x) (1) y(t) = Bcos(omega_yt-delta_y), (2) sometimes also written in ...

A list is a data structure consisting of an ordered set of elements, each of which may be a number, another list, etc. A list is usually denoted (a_1, a_2, ..., a_n) or ...

A statement letter or a negation of a statement letter (Mendelson 1997, p. 30).

The symbol o(x), pronounced "little-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n ...

Little-omega notation is the inverse of the Landau symbol o, i.e., f(n) in o(phi(n)) <==> phi(n) in omega(f(n)).

A roll of 4 on a pair of six-sided dice in the game of craps (Gardner 1978, p. 256). The probability of rolling "a little Joe" is 1/12, or 8.333...%. A roll of "4 the hard ...