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To find the motion of a rectangular membrane with sides of length L_x and L_y (in the absence of gravity), use the two-dimensional wave equation ...

An integer whose decimal digits contain no zeros is said to be zerofree. The first few positive zerofree integers are 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 15, 16, 17, ...

The term "integral" can refer to a number of different concepts in mathematics. The most common meaning is the the fundamenetal object of calculus corresponding to summing ...

The Jacobi elliptic functions are standard forms of elliptic functions. The three basic functions are denoted cn(u,k), dn(u,k), and sn(u,k), where k is known as the elliptic ...

A power is an exponent to which a given quantity is raised. The expression x^a is therefore known as "x to the ath power." A number of powers of x are plotted above (cf. ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

The Catalan numbers on nonnegative integers n are a set of numbers that arise in tree enumeration problems of the type, "In how many ways can a regular n-gon be divided into ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

Let x=[a_0;a_1,...]=a_0+1/(a_1+1/(a_2+1/(a_3+...))) (1) be the simple continued fraction of a "generic" real number x, where the numbers a_i are the partial denominator. ...

Kontsevich's integral is a far-reaching generalization of the Gauss integral for the linking number, and provides a tool to construct the universal Vassiliev invariant of a ...