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Functions which can be expressed in terms of Legendre functions of the first and second kinds. See Abramowitz and Stegun (1972, p. 337). P_(-1/2+ip)(costheta) = (1) = ...

Attractive compounds can be constructed from the cube 3-compounds and their octahedron 3-compound duals. One is illustrated above. This compound will be implemented in a ...

The term in logic used to describe the operation commonly known as OR. A literal is considered a (degenerate) disjunction (Mendelson 1997, p. 30). The Wolfram Language ...

The double bar symbol | is used to denote certain kinds of norms in mathematics (e.g., ||x|| or ||x||_2). It is also used to denote parallel lines, as in A∥B, and in an older ...

A group action phi:G×X->X is called faithful if there are no group elements g (except the identity element) such that gx=x for all x in X. Equivalently, the map phi induces ...

If A is a unital Banach algebra where every nonzero element is invertible, then A is the algebra of complex numbers.

A method for constructing magic squares of odd order.

The maximal independence polynomial I_G(x) for the graph G may be defined as the polynomial I_G(x)=sum_(k=i(G))^(alpha(G))s_kx^k, where i(G) is the lower independence number, ...

A version of nim-like games in which the player taking the last piece is the loser. For most impartial games, this form is much harder to analyze, but it requires only a ...

The symbol × used to denote multiplication, i.e., a×b denotes a times b. The symbol × is also used to denote a group direct product, a Cartesian product, or a direct product ...