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A merge sort (or collation sort) is the combination of two or more ordered lists into a single ordered list (Knuth 1998, p. 158). Merge sorting was one of the first methods ...

A Fourier series-like expansion of a twice continuously differentiable function f(x)=1/2a_0+sum_(n=1)^inftya_nJ_0(nx) (1) for 0<x<pi, where J_0(x) is a zeroth order Bessel ...

A number (usually base 10 unless specified otherwise) which has no digitaddition generator. Such numbers were originally called Colombian numbers (S. 1974). There are ...

The spherical curve taken by a ship which travels from the south pole to the north pole of a sphere while keeping a fixed (but not right) angle with respect to the meridians. ...

The Weierstrass zeta function zeta(z;g_2,g_3) is the quasiperiodic function defined by (dzeta(z;g_2,g_3))/(dz)=-P(z;g_2,g_3), (1) where P(z;g_2,g_3) is the Weierstrass ...

Let sopfr(n) be the sum of prime factors (with repetition) of a number n. For example, 20=2^2·5, so sopfr(20)=2+2+5=9. Then sopfr(n) for n=1, 2, ... is given by 0, 2, 3, 4, ...

An identity in calculus of variations discovered in 1868 by Beltrami. The Euler-Lagrange differential equation is (partialf)/(partialy)-d/(dx)((partialf)/(partialy_x))=0. (1) ...

If n=1,2 (mod 4), and the squarefree part of n is divisible by a prime p=3 (mod 4), then no difference set of order n exists. Equivalently, if a projective plane of order n ...

Given a set P of primes, a field K is called a class field if it is a maximal normal extension of the rationals which splits all of the primes in P, and if P is the maximal ...

Two complex numbers x=a+ib and y=c+id are multiplied as follows: xy = (a+ib)(c+id) (1) = ac+ibc+iad-bd (2) = (ac-bd)+i(ad+bc). (3) In component form, ...