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Adding a damping force proportional to x^. to the equation of simple harmonic motion, the first derivative of x with respect to time, the equation of motion for damped simple ...

Let c and d!=c be real numbers (usually taken as c=1 and d=0). The Dirichlet function is defined by D(x)={c for x rational; d for x irrational (1) and is discontinuous ...

A function f(z) is said to be doubly periodic if it has two periods omega_1 and omega_2 whose ratio omega_2/omega_1 is not real. A doubly periodic function that is analytic ...

There are two sorts of transforms known as the fractional Fourier transform. The linear fractional Fourier transform is a discrete Fourier transform in which the exponent is ...

A mathematical statement that one quantity is greater than or less than another. "a is less than b" is denoted a<b, and "a is greater than b" is denoted a>b. "a is less than ...

The variable phi (also denoted am(u,k)) used in elliptic functions and elliptic integrals is called the amplitude (or Jacobi amplitude). It can be defined by phi = am(u,k) ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

A Lyapunov function is a scalar function V(y) defined on a region D that is continuous, positive definite, V(y)>0 for all y!=0), and has continuous first-order partial ...

A type of integral containing gamma functions in its integrand. A typical such integral is given by ...

A p-variate multivariate normal distribution (also called a multinormal distribution) is a generalization of the bivariate normal distribution. The p-multivariate ...