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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 conjecture that there are only finitely many triples of relatively prime integer powers x^p, y^q, z^r for which x^p+y^q=z^r (1) with 1/p+1/q+1/r<1. (2) Darmon and Merel ...

Let s=1/(sqrt(2pi))[Gamma(1/4)]^2=5.2441151086... (1) (OEIS A064853) be the arc length of a lemniscate with a=1. Then the lemniscate constant is the quantity L = 1/2s (2) = ...

For every positive integer n, there is a unique finite sequence of distinct nonconsecutive (not necessarily positive) integers k_1, ..., k_m such that ...

A quartic symmetric graph is a symmetric graph that is also quartic (i.e., regular of degree 4). The numbers of symmetric quartic graphs on n=1, 2, ... are 0, 0, 0, 0, 1, 1, ...

The Rogers-Selberg identities are a set of three analytic q-series identities of Rogers-Ramanujan-type appearing as equation 33, 32, and 31 in Slater (1952), A(q) = ...

Approximations to Catalan's constant include K approx (9/(10))^(5/6) (1) approx ln(ln892)-1 (2) approx (1/(96))^(1/52) (3) approx (4/(51))^(1/29) (4) approx ...

Togliatti surfaces are quintic surfaces having the maximum possible number of ordinary double points (31). A related surface sometimes known as the dervish can be defined by ...

A double factorial prime is a prime number of the form n!!+/-1, where n!! is a double factorial. n!!-1 is prime for n=3, 4, 6, 8, 16, 26, 64, 82, 90, 118, 194, 214, 728, ... ...

The first singular value k_1 of the elliptic integral of the first kind K(k), corresponding to K^'(k_1)=K(k_1), (1) is given by k_1 = 1/(sqrt(2)) (2) k_1^' = 1/(sqrt(2)). (3) ...