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There are a number of equations known as the Riccati differential equation. The most common is z^2w^('')+[z^2-n(n+1)]w=0 (1) (Abramowitz and Stegun 1972, p. 445; Zwillinger ...

The Remez algorithm (Remez 1934), also called the Remez exchange algorithm, is an application of the Chebyshev alternation theorem that constructs the polynomial of best ...

In analysis, the phrase "Riesz-Fischer theorem" is used to describe a number of results concerning the convergence of Cauchy sequences in L-p spaces. The theorem is named for ...

Smale's problems are a list of 18 challenging problems for the twenty-first century proposed by Field medalist Steven Smale. These problems were inspired in part by Hilbert's ...

Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...

The nth Beraha constant (or number) is given by B(n)=2+2cos((2pi)/n). B(5) is phi+1, where phi is the golden ratio, B(7) is the silver constant, and B(10)=phi+2. The ...

The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

The Thue-Morse sequence, also called the Morse-Thue sequence or Prouhet-Thue-Morse sequence (Allouche and Cosnard 2000), is one of a number of related sequences of numbers ...

A quartic graph is a graph which is 4-regular. The unique quartic graph on five nodes is the complete graph K_5, and the unique quartic graph on six nodes is the octahedral ...