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The expected number of trials needed to collect a complete set of n different objects when picked at random with repetition is nH_n (Havil 2003, p. 131). For n=1, 2, ..., the ...

The confluent hypergeometric function of the first kind _1F_1(a;b;z) is a degenerate form of the hypergeometric function _2F_1(a,b;c;z) which arises as a solution the ...

There are at least two meanings on the word congruent in mathematics. Two geometric figures are said to be congruent if one can be transformed into the other by an isometry ...

The phrase "convergence in mean" is used in several branches of mathematics to refer to a number of different types of sequential convergence. In functional analysis, ...

A notation for polyhedra which begins by specifying a "seed" polyhedron using a capital letter. The Platonic solids are denoted T (tetrahedron), O (octahedron), C (cube), I ...

A covering map (also called a covering or projection) is a surjective open map f:X->Y that is locally a homeomorphism, meaning that each point in X has a neighborhood that is ...

Let F be the Maclaurin series of a meromorphic function f with a finite or infinite number of poles at points z_k, indexed so that 0<|z_1|<=|z_2|<=|z_3|<=..., then a pole ...

There are a number of attractive cube 20-compounds that can be constructed by taking the duals of the octahedra in the two octahedron 20-compounds. The second of these was ...

There are a number of attractive cube 25-compounds. One can be constructed from the vertices of the second dodecahedron 6-compound (or second tetrahedron 50-compound) and ...

There are a number of attractive polyhedron compounds consisting of five cubes. The first of these (left figures) consists of the arrangement of five cubes in the polyhedron ...