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A function whose value increases more quickly than any polynomial is said to be an exponentially increasing function. The prototypical example is the function e^x, plotted ...

Given two circles, draw the tangents from the center of each circle to the sides of the other. Then the line segments AB and CD are of equal length. The theorem can be proved ...

A number of the form 2^n-1 obtained by setting x=1 in a Fermat-Lucas polynomial, more commonly known as a Mersenne number.

The ring of fractions of an integral domain. The field of fractions of the ring of integers Z is the rational field Q, and the field of fractions of the polynomial ring ...

Let M^n be an n-manifold and let F={F_alpha} denote a partition of M into disjoint pathwise-connected subsets. Then if F is a foliation of M, each F_alpha is called a leaf ...

A fractional clique of a graph G is a nonnegative real function on the vertices of G such that sum of the values on the vertices of any independent set is at most one. The ...

A smooth curve which corresponds to the limiting case of a histogram computed for a frequency distribution of a continuous distribution as the number of data points becomes ...

A finite extension K=Q(z)(w) of the field Q(z) of rational functions in the indeterminate z, i.e., w is a root of a polynomial a_0+a_1alpha+a_2alpha^2+...+a_nalpha^n, where ...

Given two univariate polynomials of the same order whose first p coefficients (but not the first p-1) are 0 where the coefficients of the second approach the corresponding ...

The abscissas of the N-point Gaussian quadrature formula are precisely the roots of the orthogonal polynomial for the same interval and weighting function.