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Whipple derived a great many identities for generalized hypergeometric functions, many of which are consequently known as Whipple's identities (transformations, etc.). Among ...

The q-analog of the binomial theorem (1-z)^n=1-nz+(n(n-1))/(1·2)z^2-(n(n-1)(n-2))/(1·2·3)z^3+... (1) is given by (1-z/(q^n))(1-z/(q^(n-1)))...(1-z/q) ...

The van der Grinten projection is a map projection given by the transformation x = (1) y = sgn(phi)(pi|PQ-Asqrt((A^2+1)(P^2+A^2)-Q^2)|)/(P^2+A^2), (2) where A = ...

A magic square is a square array of numbers consisting of the distinct positive integers 1, 2, ..., n^2 arranged such that the sum of the n numbers in any horizontal, ...

One of the Zermelo-Fraenkel axioms, also known as the axiom of regularity (Rubin 1967, Suppes 1972). In the formal language of set theory, it states that x!=emptyset=> exists ...

Vizing's theorem states that a graph can be edge-colored in either Delta or Delta+1 colors, where Delta is the maximum vertex degree of the graph. A graph with edge chromatic ...

In general, the word "complement" refers to that subset F^' of some set S which excludes a given subset F. Taking F and its complement F^' together then gives the whole of ...

There are three theorems related to pedal circles that go under the collective title of the Fontené theorems. The first Fontené theorem lets DeltaABC be a triangle and P an ...

Let A be an n×n real square matrix with n>=2 such that |sum_(i=1)^nsum_(j=1)^na_(ij)s_it_j|<=1 (1) for all real numbers s_1, s_2, ..., s_n and t_1, t_2, ..., t_n such that ...

Let |A| denote the cardinal number of set A, then it follows immediately that |A union B|=|A|+|B|-|A intersection B|, (1) where union denotes union, and intersection denotes ...