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Differential Equations

The h-statistic h_r is the unique symmetric unbiased estimator for a central moment of a distribution <h_r>=mu_r. (1) In addition, the variance var(h_r)=<(h_r-mu_r)^2> (2) is ...

A q-analog of Zeilberger's algorithm.

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

The apeirogon is an extension of the definition of regular polygon to a figure with an infinite number of sides. Its Schläfli symbol is {infty}. The apeirogon can produce a ...

There are a number of meanings for the word "arc" in mathematics. In general, an arc is any smooth curve joining two points. The length of an arc is known as its arc length. ...

An array is a "list of lists" with the length of each level of list the same. The size (sometimes called the "shape") of a d-dimensional array is then indicated as ...

Two circles may intersect in two imaginary points, a single degenerate point, or two distinct points. The intersections of two circles determine a line known as the radical ...

Given a sequence {a_n}_(n=1)^infty, a formal power series f(s) = sum_(n=1)^(infty)(a_n)/(n^s) (1) = a_1+(a_2)/(2^s)+(a_3)/(3^s)+... (2) is called the Dirichlet generating ...

The distribution function D(x), also called the cumulative distribution function (CDF) or cumulative frequency function, describes the probability that a variate X takes on a ...