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A generalized hypergeometric function _pF_q(a_1,...,a_p;b_1,...,b_q;x) is a function which can be defined in the form of a hypergeometric series, i.e., a series for which the ...

The identity matrix is a the simplest nontrivial diagonal matrix, defined such that I(X)=X (1) for all vectors X. An identity matrix may be denoted 1, I, E (the latter being ...

A set-theoretic term having a number of different meanings. Fraenkel (1953, p. 37) used the term as a synonym for "finite set." However, according to Russell's definition ...

The infimum is the greatest lower bound of a set S, defined as a quantity m such that no member of the set is less than m, but if epsilon is any positive quantity, however ...

An interpretation of first-order logic consists of a non-empty domain D and mappings for function and predicate symbols. Every n-place function symbol is mapped to a function ...

Given a function f(x), its inverse f^(-1)(x) is defined by f(f^(-1)(x))=f^(-1)(f(x))=x. (1) Therefore, f(x) and f^(-1)(x) are reflections about the line y=x. In the Wolfram ...

Roughly speaking, isospectral manifolds are drums that sound the same, i.e., have the same eigenfrequency spectrum. Two drums with differing area, perimeter, or genus can ...

A tensor which has the same components in all rotated coordinate systems. All rank-0 tensors (scalars) are isotropic, but no rank-1 tensors (vectors) are. The unique rank-2 ...

A theorem giving a criterion for an origami construction to be flat. Kawasaki's theorem states that a given crease pattern can be folded to a flat origami iff all the ...

C. Kimberling has extensively tabulated and enumerated the properties of triangle centers (Kimberling 1994, 1998, and online), denoting the nth center in his numbering scheme ...