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The first few values of product_(k=1)^(n)k! (known as a superfactorial) for n=1, 2, ... are given by 1, 2, 12, 288, 34560, 24883200, ... (OEIS A000178). The first few ...

If {a_j} subset= D(0,1) (with possible repetitions) satisfies sum_(j=1)^infty(1-|a_j|)<=infty, where D(0,1) is the unit open disk, and no a_j=0, then there is a bounded ...

The amazing polynomial identity communicated by Euler in a letter to Goldbach on April 12, 1749 (incorrectly given as April 15, 1705--before Euler was born--in Conway and Guy ...

The categorical notion which is dual to product. The coproduct of a family {X_i}_(i in I) of objects of a category is an object C=coproduct_(i in I)X_i, together with a ...

Given a commutative ring R, an R-algebra H is a Hopf algebra if it has additional structure given by R-algebra homomorphisms Delta:H->H tensor _RH (1) (comultiplication) and ...

An operator A^~ is said to be antiunitary if it satisfies: <A^~f_1|A^~f_2> = <f_1|f_2>^_ (1) A^~[f_1(x)+f_2(x)] = A^~f_1(x)+A^~f_2(x) (2) A^~cf(x) = c^_A^~f(x), (3) where ...

Suppose that E(G) (the commuting product of all components of G) is simple and G contains a semisimple group involution. Then there is some semisimple group involution x such ...

A finite or infinite square matrix with rational entries. (If the matrix is infinite, all but a finite number of entries in each row must be 0.) The sum or product of two ...

The multiplicative subgroup of all elements in the product of the multiplicative groups k_nu^× whose absolute value is 1 at all but finitely many nu, where k is a number ...

An integer kappa equal to 0 or 1 which vanishes iff the product manifold M^4×R can be given a smooth structure. Here, M^n is a compact connected topological four-manifold.