Search Results for ""

A Chaitin's constant, also called a Chaitin omega number, introduced by Chaitin (1975), is the halting probability of a universal prefix-free (self-delimiting) Turing ...

An equation is said to be a closed-form solution if it solves a given problem in terms of functions and mathematical operations from a given generally-accepted set. For ...

The word "convergent" has a number of different meanings in mathematics. Most commonly, it is an adjective used to describe a convergent sequence or convergent series, where ...

The Dirichlet beta function is defined by the sum beta(x) = sum_(n=0)^(infty)(-1)^n(2n+1)^(-x) (1) = 2^(-x)Phi(-1,x,1/2), (2) where Phi(z,s,a) is the Lerch transcendent. The ...

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

Euclid's second theorem states that the number of primes is infinite. The proof of this can be accomplished using the numbers E_n = 1+product_(i=1)^(n)p_i (1) = 1+p_n#, (2) ...

The Euler-Maclaurin integration and sums formulas can be derived from Darboux's formula by substituting the Bernoulli polynomial B_n(t) in for the function phi(t). ...

Turing machines are defined by sets of rules that operate on four parameters: (state, tape cell color, operation, state). Let the states and tape cell colors be numbered and ...

The gyroid, illustrated above, is an infinitely connected periodic minimal surface containing no straight lines (Osserman 1986) that was discovered by Schoen (1970). ...

The Hadwiger number of a graph G, variously denoted eta(G) (Zelinka 1976, Ivančo 1988) or h(G) (Stiebitz 1990), is the number of vertices in the largest complete minor of G ...