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The tractrix arises in the following problem posed to Leibniz: What is the path of an object starting off with a vertical offset when it is dragged along by a string of ...

Analytic continuation (sometimes called simply "continuation") provides a way of extending the domain over which a complex function is defined. The most common application is ...

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. ...

There are several closely related results that are variously known as the binomial theorem depending on the source. Even more confusingly a number of these (and other) ...

A branch cut is a curve (with ends possibly open, closed, or half-open) in the complex plane across which an analytic multivalued function is discontinuous. For convenience, ...

The conjecture made by Belgian mathematician Eugène Charles Catalan in 1844 that 8 and 9 (2^3 and 3^2) are the only consecutive powers (excluding 0 and 1). In other words, ...

The Cauchy principal value of a finite integral of a function f about a point c with a<=c<=b is given by ...

Let Pi be a permutation of n elements, and let alpha_i be the number of permutation cycles of length i in this permutation. Picking Pi at random, it turns out that ...

If Li_2(x) denotes the usual dilogarithm, then there are two variants that are normalized slightly differently, both called the Rogers L-function (Rogers 1907). Bytsko (1999) ...

secz is the trigonometric function defined by secz = 1/(cosz) (1) = 2/(e^(iz)+e^(-iz)), (2) where cosz is the cosine. The secant is implemented in the Wolfram Language as ...