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By analogy with the log sine function, define the log cosine function by C_n=int_0^(pi/2)[ln(cosx)]^ndx. (1) The first few cases are given by C_1 = -1/2piln2 (2) C_2 = ...

The Lorentz group is the group L of time-preserving linear isometries of Minkowski space R^((3,1)) with the Minkowski metric dtau^2=-(dx^0)^2+(dx^1)^2+(dx^2)^2+(dx^3)^2 ...

A method for finding roots which defines P_j(x)=(P(x))/((x-x_1)...(x-x_j)), (1) so the derivative is (2) One step of Newton's method can then be written as ...

The mean distance of a (connected) graph is the mean of the elements of its graph distance matrix. Closed forms for some classes of named graphs are given in the following ...

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 ...

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 ...

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 ...