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The 34 distinct convergent hypergeometric series of order two enumerated by Horn (1931) and corrected by Borngässer (1933). There are 14 complete series for which ...

A function is said to be modular (or "elliptic modular") if it satisfies: 1. f is meromorphic in the upper half-plane H, 2. f(Atau)=f(tau) for every matrix A in the modular ...

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) = ...

A block matrix is a matrix that is defined using smaller matrices, called blocks. For example, [A B; C D], (1) where A, B, C, and D are themselves matrices, is a block ...

Brown numbers are pairs (m,n) of integers satisfying the condition of Brocard's problem, i.e., such that n!+1=m^2 where n! is the factorial and m^2 is a square number. Only ...

Given any assignment of n-element sets to the n^2 locations of a square n×n array, is it always possible to find a partial Latin square? The fact that such a partial Latin ...

Fermat's sandwich theorem states that 26 is the only number sandwiched between a perfect square number (5^2=25) and a perfect cubic number (3^3=27). According to Singh ...

Polysticks, sometimes also known as polyedges, are polyforms obtained from the edges of a regular grid. Square polysticks are polyforms obtained from the edges of a regular ...

That part of a positive integer left after all square factors are divided out. For example, the squarefree part of 24=2^3·3 is 6, since 6·2^2=24. For n=1, 2, ..., the first ...

A bimagic cube is a (normal) magic cube that remains magic when all its elements are squared. Of course, even a normal magic cubic becomes nonnormal (i.e., contains ...