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A sum which includes both the Jacobi triple product and the q-binomial theorem as special cases. Ramanujan's sum is ...

sum_(n=0)^(infty)(-1)^n[((2n-1)!!)/((2n)!!)]^3 = 1-(1/2)^3+((1·3)/(2·4))^3+... (1) = _3F_2(1/2,1/2,1/2; 1,1;-1) (2) = [_2F_1(1/4,1/4; 1;-1)]^2 (3) = ...

The partial differential equation u_(tt)-u_(xx)=epsilon(u_t-u_t^3).

A real function is said to be analytic if it possesses derivatives of all orders and agrees with its Taylor series in a neighborhood of every point.

A pair of consecutive primes whose digits are rearrangements of each other, first considered by A. Edwards in Aug. 2001. The first few are (1913, 1931), (18379, 18397), ...

The sum of reciprocal multifactorials can be given in closed form by the beautiful formula m(n) = sum_(n=0)^(infty)1/(n!...!_()_(k)) (1) = ...

A knot diagram in which none of the crossings are reducible.

Any system of phi(n) integers, where phi(n) is the totient function, representing all the residue classes relatively prime to n is called a reduced residue system (Nagell ...

A reduced root system is a root system R satisfying the additional property that, if alpha in R, then the only multiples of alpha in R are +/-alpha.

An extension to the Berlekamp-Massey algorithm which applies when the terms of the sequences are integers modulo some given modulus m.