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An identity graph, sometimes also known as an asymmetric graph or rigid graph (Albertson and Collins 1996), is a graph possessing a single graph automorphism. The numbers of ...

A transformation formula for continued fractions (Lorentzen and Waadeland 1992) which can, for example, be used to prove identities such as ...

Let K be a field of arbitrary characteristic. Let v:K->R union {infty} be defined by the following properties: 1. v(x)=infty<=>x=0, 2. v(xy)=v(x)+v(y) forall x,y in K, and 3. ...

Some authors define a general Airy differential equation as y^('')+/-k^2xy=0. (1) This equation can be solved by series solution using the expansions y = ...

The Copeland-Erdős constant has decimal expansion C=0.23571113... (OEIS A033308). The Earls sequence (starting position of n copies of the digit n) for e is given for n=1, 2, ...

The golden ratio has decimal expansion phi=1.618033988749894848... (OEIS A001622). It can be computed to 10^(10) digits of precision in 24 CPU-minutes on modern hardware and ...

Consider a string of length 2L plucked at the right end and fixed at the left. The functional form of this configuration is f(x)=x/(2L). (1) The components of the Fourier ...

A positive integer n>1 is quiteprime iff all primes p<=sqrt(n) satisfy |2[n (mod p)]-p|<=p+1-sqrt(p). Also define 2 and 3 to be quiteprimes. Then the first few quiteprimes ...

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 square number, also called a perfect square, is a figurate number of the form S_n=n^2, where n is an integer. The square numbers for n=0, 1, ... are 0, 1, 4, 9, 16, 25, 36, ...