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The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

The term limit comes about relative to a number of topics from several different branches of mathematics. A sequence x_1,x_2,... of elements in a topological space X is said ...

The reciprocal of the arithmetic-geometric mean of 1 and sqrt(2), G = 2/piint_0^11/(sqrt(1-x^4))dx (1) = 2/piint_0^(pi/2)(dtheta)/(sqrt(1+sin^2theta)) (2) = L/pi (3) = ...

The first Göllnitz-Gordon identity states that the number of partitions of n in which the minimal difference between parts is at least 2, and at least 4 between even parts, ...

A Euclidean number is a number which can be obtained by repeatedly solving the quadratic equation. Euclidean numbers, together with the rational numbers, can be constructed ...

The Paley graph of order q with q a prime power is a graph on q nodes with two nodes adjacent if their difference is a square in the finite field GF(q). This graph is ...

The simple continued fraction for pi is given by [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, ...] (OEIS A001203). A plot of the first 256 terms of the ...

The batman curve is a piecewise curve in the shape of the logo of the Batman superhero originally posted on reddit.com on Jul. 28, 2011. It can written as two functions, one ...

A wavelet used for filtering signals. Daubechies (1988, p. 980) has tabulated the numerical values up to order p=10.

The Kaprekar routine is an algorithm discovered in 1949 by D. R. Kaprekar for 4-digit numbers, but which can be generalized to k-digit numbers. To apply the Kaprekar routine ...