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The infimum of all number a for which |f(z)|<=exp(|z|^a) holds for all |z|>r and f an entire function, is called the order of f, denoted lambda=lambda(f) (Krantz 1999, p. ...

The Bessel functions of the first kind J_n(x) are defined as the solutions to the Bessel differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+(x^2-n^2)y=0 (1) which are ...

"Chaos" is a tricky thing to define. In fact, it is much easier to list properties that a system described as "chaotic" has rather than to give a precise definition of chaos. ...

A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of ...

The Hurwitz zeta function zeta(s,a) is a generalization of the Riemann zeta function zeta(s) that is also known as the generalized zeta function. It is classically defined by ...

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 ...

The sinc function sinc(x), also called the "sampling function," is a function that arises frequently in signal processing and the theory of Fourier transforms. The full name ...

A Brauer chain is an addition chain in which each member uses the previous member as an addend. A number n for which a shortest chain exists which is a Brauer chain is called ...

One of the operations of addition, subtraction, multiplication, division, and integer (or rational) root extraction.

An addition chain for which there is a subset H of members such that each member of the chain uses the largest element of H which is less than the member.