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A number taken to the power 2 is said to be squared, so x^2 is called "x squared." This terminology derives from the fact that the area of a square of edge length x is given ...

A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., to an n-gon for n an arbitrary positive integer. The above diagrams ...

The hyperbolic cosine integral, often called the "Chi function" for short, is defined by Chi(z)=gamma+lnz+int_0^z(cosht-1)/tdt, (1) where gamma is the Euler-Mascheroni ...

Calculus I

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

The great success mathematicians had studying hypergeometric functions _pF_q(a_1,...,a_p;b_1,...,b_q;z) for the convergent cases (p<=q+1) prompted attempts to provide ...

Stirling's approximation gives an approximate value for the factorial function n! or the gamma function Gamma(n) for n>>1. The approximation can most simply be derived for n ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...

The lemniscate functions arise in rectifying the arc length of the lemniscate. The lemniscate functions were first studied by Jakob Bernoulli and Giulio Fagnano. A historical ...

Define the Euler measure of a polyhedral set as the Euler integral of its indicator function. It is easy to show by induction that the Euler measure of a closed bounded ...