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If g is a continuous function g(x) in [a,b] for all x in [a,b], then g has a fixed point in [a,b]. This can be proven by supposing that g(a)>=a g(b)<=b (1) g(a)-a>=0 ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_7=f(x_7). Then Hardy's rule approximating the ...

Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

An inhomogeneous linear ordinary differential equation with constant coefficients is an ordinary differential equation in which coefficients are constants (i.e., not ...

An isogonal mapping is a transformation w=f(z) that preserves the magnitudes of local angles, but not their orientation. A few examples are illustrated above. A conformal ...

An integral transform which is often written as an ordinary Laplace transform involving the delta function. The Laplace transform and Dirichlet series are special cases of ...

A metric space is a set S with a global distance function (the metric g) that, for every two points x,y in S, gives the distance between them as a nonnegative real number ...

There exist lattices in n dimensions having hypersphere packing densities satisfying eta>=(zeta(n))/(2^(n-1)), where zeta(n) is the Riemann zeta function. However, the proof ...

Let f(z) be an analytic function of z, regular in the half-strip S defined by a<x<b and y>0. If f(z) is bounded in S and tends to a limit l as y->infty for a certain fixed ...

The Peano-Gosper curve is a plane-filling function originally called a "flowsnake" by R. W. Gosper and M. Gardner. Mandelbrot (1977) subsequently coined the name Peano-Gosper ...