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The extangents circle is the circumcircle of the extangents triangle. Its center function is a complicated 9th-order polynomial and its circle function is a complicated ...

Let T_n(x) be an arbitrary trigonometric polynomial T_n(x)=1/2a_0+{sum_(k=1)^n[a_kcos(kx)+b_ksin(kx)]} (1) with real coefficients, let f be a function that is integrable over ...

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...

Let p>3 be a prime number, then 4(x^p-y^p)/(x-y)=R^2(x,y)-(-1)^((p-1)/2)pS^2(x,y), where R(x,y) and S(x,y) are homogeneous polynomials in x and y with integer coefficients. ...

The numbers H_n=H_n(0), where H_n(x) is a Hermite polynomial, may be called Hermite numbers. For n=0, 1, ..., the first few are 1, 0, -2, 0, 12, 0, -120, 0, 1680, 0, ... ...

Horowitz reduction is used in indefinite integration to reduce a rational function into polynomial and logarithmic parts. The polynomial part is then trivially integrated, ...

The idempotent numbers are given by B_(n,k)(1,2,3,...)=(n; k)k^(n-k), where B_(n,k) is a Bell polynomial and (n; k) is a binomial coefficient. A table of the first few is ...

An independent edge set (also called a matching) of a graph G is a subset of the edges such that no two edges in the subset share a vertex of G (Skiena 1990, p. 219). The ...

A quantity which remains unchanged under certain classes of transformations. Invariants are extremely useful for classifying mathematical objects because they usually reflect ...

A complicated polynomial root-finding algorithm which is used in the IMSL® (IMSL, Houston, TX) library and which Press et al. (1992) describe as "practically a standard in ...