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The golden ratio, also known as the divine proportion, golden mean, or golden section, is a number often encountered when taking the ratios of distances in simple geometric ...

A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., n^2 arranged such that the sum of the n numbers in any horizontal, ...

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

There are four varieties of Airy functions: Ai(z), Bi(z), Gi(z), and Hi(z). Of these, Ai(z) and Bi(z) are by far the most common, with Gi(z) and Hi(z) being encountered much ...

An algorithm is a specific set of instructions for carrying out a procedure or solving a problem, usually with the requirement that the procedure terminate at some point. ...

The arithmetic-geometric mean agm(a,b) of two numbers a and b (often also written AGM(a,b) or M(a,b)) is defined by starting with a_0=a and b_0=b, then iterating a_(n+1) = ...

The arithmetic mean of a set of values is the quantity commonly called "the" mean or the average. Given a set of samples {x_i}, the arithmetic mean is x^_=1/Nsum_(i=1)^Nx_i. ...

Solutions to the associated Laguerre differential equation with nu!=0 and k an integer are called associated Laguerre polynomials L_n^k(x) (Arfken 1985, p. 726) or, in older ...

The word "base" in mathematics is used to refer to a particular mathematical object that is used as a building block. The most common uses are the related concepts of the ...

There are two definitions of Bernoulli polynomials in use. The nth Bernoulli polynomial is denoted here by B_n(x) (Abramowitz and Stegun 1972), and the archaic form of the ...