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The quantities obtained from cubic, hexagonal, etc., lattice sums, evaluated at s=1, are called Madelung constants. For cubic lattice sums ...

The Meijer G-function is a very general function which reduces to simpler special functions in many common cases. The Meijer G-function is defined by (1) where Gamma(s) is ...

The transformation of a sequence a_1, a_2, ... with a_n=sum_(d|n)b_d (1) into the sequence b_1, b_2, ... via the Möbius inversion formula, b_n=sum_(d|n)mu(n/d)a_d. (2) The ...

A normalized form of the cumulative normal distribution function giving the probability that a variate assumes a value in the range [0,x], ...

The Pierce expansion, or alternated Egyptian product, of a real number 0<x<1 is the unique increasing sequence {a_1,a_2,...} of positive integers a_i such that ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...

The Rhind papyrus is a famous document from the Egyptian Middle Kingdom that dates to 1650 BC. It was purchased by Henry Rhind in Egypt in 1858, and placed in the British ...

A sequence s_n(x) is called a Sheffer sequence iff its generating function has the form sum_(k=0)^infty(s_k(x))/(k!)t^k=A(t)e^(xB(t)), (1) where A(t) = A_0+A_1t+A_2t^2+... ...

A solvable group is a group having a normal series such that each normal factor is Abelian. The special case of a solvable finite group is a group whose composition indices ...

Two trains are on the same track a distance 100 km apart heading towards one another, each at a speed of 50 km/h. A fly starting out at the front of one train, flies towards ...