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A seminorm is a function on a vector space V, denoted ||v||, such that the following conditions hold for all v and w in V, and any scalar c. 1. ||v||>=0, 2. ||cv||=|c|||v||, ...

A powerful numerical integration technique which uses k refinements of the extended trapezoidal rule to remove error terms less than order O(N^(-2k)). The routine advocated ...

The Legendre symbol is a number theoretic function (a/p) which is defined to be equal to +/-1 depending on whether a is a quadratic residue modulo p. The definition is ...

Lehmer's totient problem asks if there exist any composite numbers n such that phi(n)|(n-1), where phi(n) is the totient function? No such numbers are known. However, any ...

Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

In general, a singularity is a point at which an equation, surface, etc., blows up or becomes degenerate. Singularities are often also called singular points. Singularities ...

The angles mpi/n (with m,n integers) for which the trigonometric functions may be expressed in terms of finite root extraction of real numbers are limited to values of m ...

Exponential decay is the decrease in a quantity N according to the law N(t)=N_0e^(-lambdat) (1) for a parameter t and constant lambda (known as the decay constant), where e^x ...

The polynomials M_k(x;delta,eta) which form the Sheffer sequence for g(t) = {[1+deltaf(t)]^2+[f(t)]^2}^(eta/2) (1) f(t) = tan(t/(1+deltat)) (2) which have generating function ...

A hypergeometric class of orthogonal polynomials defined by R_n(lambda(x);alpha,beta,gamma,delta) =_4F_3(-n,n+alpha+beta+1,-x,x+gamma+delta+1; alpha+1,beta+delta+1,gamma+1;1) ...