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The Mercator series, also called the Newton-Mercator series (Havil 2003, p. 33), is the Taylor series for the natural logarithm ln(1+x) = sum_(k=1)^(infty)((-1)^(k+1))/kx^k ...

An inequality which implies the correctness of the Robertson conjecture (Milin 1964). de Branges (1985) proved this conjecture, which led to the proof of the full Bieberbach ...

A minimum vertex cut of a graph is a vertex cut of smallest possible size. A vertex cut set of size 1 in a connected graph corresponds to an articulation vertex. The size of ...

If a function analytic at the origin has no singularities other than poles for finite x, and if we can choose a sequence of contours C_m about z=0 tending to infinity such ...

A modular inverse of an integer b (modulo m) is the integer b^(-1) such that bb^(-1)=1 (mod m). A modular inverse can be computed in the Wolfram Language using PowerMod[b, ...

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 ...

The Morgan-Voyce polynomials are polynomials related to the Brahmagupta and Fibonacci polynomials. They are defined by the recurrence relations b_n(x) = ...

What is the longest ladder that can be moved around a right-angled hallway of unit width? For a straight, rigid ladder, the answer is 2sqrt(2), which allows the ladder to ...

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 ...

A generalization of the factorial and double factorial, n! = n(n-1)(n-2)...2·1 (1) n!! = n(n-2)(n-4)... (2) n!!! = n(n-3)(n-6)..., (3) etc., where the products run through ...