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The Feigenbaum constant delta is a universal constant for functions approaching chaos via period doubling. It was discovered by Feigenbaum in 1975 (Feigenbaum 1979) while ...

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 generalized minimal residual (GMRES) method (Saad and Schultz 1986) is an extension of the minimal residual method (MINRES), which is only applicable to symmetric ...

A mathematical procedure for finding the best-fitting curve to a given set of points by minimizing the sum of the squares of the offsets ("the residuals") of the points from ...

The Lucas numbers are the sequence of integers {L_n}_(n=1)^infty defined by the linear recurrence equation L_n=L_(n-1)+L_(n-2) (1) with L_1=1 and L_2=3. The nth Lucas number ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

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 ...

In his Meditationes algebraicae, Waring (1770, 1782) proposed a generalization of Lagrange's four-square theorem, stating that every rational integer is the sum of a fixed ...

The pathological function f_a(x)=sum_(k=1)^infty(sin(pik^ax))/(pik^a) (originally defined for a=2) that is continuous but differentiable only on a set of points of measure ...