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Householder (1953) first considered the matrix that now bears his name in the first couple of pages of his book. A Householder matrix for a real vector v can be implemented ...

The identity function id(x) is the function id(x)=x which assigns every real number x to the same real number x. It is identical to the identity map. The identity function is ...

If, after constructing a difference table, no clear pattern emerges, turn the paper through an angle of 60 degrees and compute a new table. If necessary, repeat the process. ...

Jonquière's relation, sometimes also spelled "Joncquière's relation" (Erdélyi et al. 1981, p. 31), states ...

The complex second-order ordinary differential equation x^2y^('')+xy^'-(ix^2+nu^2)y=0 (1) (Abramowitz and Stegun 1972, p. 379; Zwillinger 1997, p. 123), whose solutions can ...

Let F be the set of complex analytic functions f defined on an open region containing the closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each f in ...

The spherical harmonics form a complete orthogonal system, so an arbitrary real function f(theta,phi) can be expanded in terms of complex spherical harmonics by ...

Let A be an involutive algebra over the field C of complex numbers with involution xi|->xi^♯. Then A is a left Hilbert algebra if A has an inner product <·,·> satisfying: 1. ...

A Lehmer number is a number generated by a generalization of a Lucas sequence. Let alpha and beta be complex numbers with alpha+beta = sqrt(R) (1) alphabeta = Q, (2) where Q ...

A minimal surface that contains lemniscates as geodesics which is given by the parametric equations x = R[sqrt(2)cos(1/3zeta)sqrt(cos(2/3zeta))] (1) y = ...