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A random walk is a sequence of discrete steps in which each step is randomly taken subject to some set of restrictions in allowed directions and step lengths. Random walks ...

Stratton (1935), Chu and Stratton (1941), and Rhodes (1970) define the spheroidal functions as those solutions of the differential equation (1) that remain finite at the ...

A figurate number Te_n of the form Te_n = sum_(k=1)^(n)T_k (1) = 1/6n(n+1)(n+2) (2) = (n+2; 3), (3) where T_k is the kth triangular number and (n; m) is a binomial ...

For a single variate X having a distribution P(x) with known population mean mu, the population variance var(X), commonly also written sigma^2, is defined as ...

An algorithm which finds a polynomial recurrence for terminating hypergeometric identities of the form sum_(k)(n; ...

A (-1,1)-matrix is a matrix whose elements consist only of the numbers -1 or 1. For an n×n (-1,1)-matrix, the largest possible determinants (Hadamard's maximum determinant ...

Let L be a nontrivial bounded lattice (or a nontrivial complemented lattice, etc.). If every nonconstant lattice homomorphism defined on L is 0,1-separating, then L is a ...

The number one (1), also called "unity," is the first positive integer. It is an odd number. Although the number 1 used to be considered a prime number, it requires special ...

The 11-cell is a regular 4-dimensional structure that cannot be represented in 3-dimensional space in any reasonable way and is highly self-intersecting even in 4-dimensional ...

The quantity twelve (12) is sometimes known as a dozen. It is in turn one twelfth of a gross. Base-12 is known as duodecimal. The Schoolhouse Rock segment "Little Twelvetoes" ...