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The second theorem of Mertens states that the asymptotic form of the harmonic series for the sum of reciprocal primes is given by sum_(p<=x)1/p=lnlnx+B_1+o(1), where p is a ...

The study of the inner structure of a mathematical theory considered as a whole. It deals with the general properties of the rules according to which the objects of a certain ...

The fundamental theorem of game theory which states that every finite, zero-sum, two-person game has optimal mixed strategies. It was proved by John von Neumann in 1928. ...

In many computer languages (such as FORTRAN or the Wolfram Language), the common residue of b (mod m) is written mod(b, m) (FORTRAN) or Mod[b, m] (Wolfram Language). The ...

A monotonic function is a function which is either entirely nonincreasing or nondecreasing. A function is monotonic if its first derivative (which need not be continuous) ...

In 1979, Conway and Norton discovered an unexpected intimate connection between the monster group M and the j-function. The Fourier expansion of j(tau) is given by (1) (OEIS ...

Let E be the largest and e the smallest power of l in the HOMFLY polynomial of an oriented link, and i be the braid index. Then the Morton-Franks-Williams inequality holds, ...

The sequence of numbers which are sums of distinct powers of 4. The first few are 0, 1, 4, 5, 16, 17, 20, 21, 64, 65, 68, 69, 80, 81, 84, ... (OEIS A000695). These numbers ...

Müntz's theorem is a generalization of the Weierstrass approximation theorem, which states that any continuous function on a closed and bounded interval can be uniformly ...

Symbols used to identify irreducible representations of groups: A= singly degenerate state which is symmetric with respect to rotation about the principal C_n axis, B= singly ...