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A hypergeometric function in which one parameter changes by +1 or -1 is said to be contiguous. There are 26 functions contiguous to _2F_1(a,b;c;x) taking one pair at a time. ...

For a simple continued fraction x=[a_0,a_1,...] with convergents p_n/q_n, the fundamental recurrence relation is given by p_nq_(n-1)-p_(n-1)q_n=(-1)^(n+1).

An algorithm for computing an Egyptian fraction, called the Farey sequence method by Bleicher (1972).

A set S in a vector space over R is called a convex set if the line segment joining any pair of points of S lies entirely in S.

The look and say sequence generated from a starting digit of 3, as given by Vardi (1991).

A sphere with four punctures occurring where a knot passes through the surface.

A countable set is a set that is either finite or denumerable. However, some authors (e.g., Ciesielski 1997, p. 64) use the definition "equipollent to the finite ordinals," ...

A covariant tensor of rank 1, more commonly called a one-form (or "bra").

A standard form of the linear programming problem of maximizing a linear function over a convex polyhedron is to maximize c·x subject to mx<=b and x>=0, where m is a given ...

In the above figure, let E be the intersection of AD and BC and specify that AB∥EF∥CD. Then 1/(AB)+1/(CD)=1/(EF). A beautiful related theorem due to H. Stengel can be stated ...