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A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open unit ball in R^n). ...

A parabola (plural "parabolas"; Gray 1997, p. 45) is the set of all points in the plane equidistant from a given line L (the conic section directrix) and a given point F not ...

Subtraction is the operation of taking the difference d=x-y of two numbers x and y. Here, x is called the minuend, y is called the subtrahend, and the symbol between the x ...

A helix, sometimes also called a coil, is a curve for which the tangent makes a constant angle with a fixed line. The shortest path between two points on a cylinder (one not ...

The permanent is an analog of a determinant where all the signs in the expansion by minors are taken as positive. The permanent of a matrix A is the coefficient of x_1...x_n ...

Let B_t={B_t(omega)/omega in Omega}, t>=0, be one-dimensional Brownian motion. Integration with respect to B_t was defined by Itô (1951). A basic result of the theory is that ...

The asymptotic series for the gamma function is given by (1) (OEIS A001163 and A001164). The coefficient a_n of z^(-n) can given explicitly by ...

Polynomials b_n(x) which form a Sheffer sequence with g(t) = t/(e^t-1) (1) f(t) = e^t-1, (2) giving generating function sum_(k=0)^infty(b_k(x))/(k!)t^k=(t(t+1)^x)/(ln(1+t)). ...

The term "biquadratic equation" is sometimes used to as a synonym for quartic equation (Beyer 1987b, p. 34), but perhaps more commonly (e.g., Hazewinkel 1988; Gellert et al. ...

The central beta function is defined by beta(p)=B(p,p), (1) where B(p,q) is the beta function. It satisfies the identities beta(p) = 2^(1-2p)B(p,1/2) (2) = ...