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A cumulative product is a sequence of partial products of a given sequence. For example, the cumulative products of the sequence {a,b,c,...}, are a, ab, abc, .... Cumulative ...

A rewriting of a given quantity (e.g., a matrix) in terms of a combination of "simpler" quantities.

Define g(k) as the quantity appearing in Waring's problem, then Euler conjectured that g(k)=2^k+|_(3/2)^k_|-2, where |_x_| is the floor function.

A game in which each player has a finite number of moves and a finite number of choices at each move.

Consider a square wave f(x) of length 2L. Over the range [0,2L], this can be written as f(x)=2[H(x/L)-H(x/L-1)]-1, (1) where H(x) is the Heaviside step function. Since ...

The convex hull of two or more functions is the largest function that is concave from above and does not exceed the given functions.

A multiple series is a series involving sums over more than one index.

Amazingly, the distribution of a difference of two normally distributed variates X and Y with means and variances (mu_x,sigma_x^2) and (mu_y,sigma_y^2), respectively, is ...

The distribution of a product of two normally distributed variates X and Y with zero means and variances sigma_x^2 and sigma_y^2 is given by P_(XY)(u) = ...

Given two distributions Y and X with joint probability density function f(x,y), let U=Y/X be the ratio distribution. Then the distribution function of u is D(u) = P(U<=u) (1) ...