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The dihedral group D_6 gives the group of symmetries of a regular hexagon. The group generators are given by a counterclockwise rotation through pi/3 radians and reflection ...

The direct limit, also called a colimit, of a family of R-modules is the dual notion of an inverse limit and is characterized by the following mapping property. For a ...

where _5F_4(a,b,c,d,e;f,g,h,i;z) is a generalized hypergeometric function and Gamma(z) is the gamma function. Bailey (1935, pp. 25-26) called the Dougall-Ramanujan identity ...

Elliptic geometry is a non-Euclidean geometry with positive curvature which replaces the parallel postulate with the statement "through any point in the plane, there exist no ...

The term energy has an important physical meaning in physics and is an extremely useful concept. There are several forms energy defined in mathematics. In measure theory, let ...

The triangle of numbers A_(n,k) given by A_(n,1)=A_(n,n)=1 (1) and the recurrence relation A_(n+1,k)=kA_(n,k)+(n+2-k)A_(n,k-1) (2) for k in [2,n], where A_(n,k) are shifted ...

An exterior angle beta of a polygon is the angle formed externally between two adjacent sides. It is therefore equal to 2pi-alpha, where alpha is the corresponding internal ...

The formal term used for a collection of objects. It is denoted {a_i}_(i in I) (but other kinds of brackets can be used as well), where I is a nonempty set called the index ...

A fiber of a map f:X->Y is the preimage of an element y in Y. That is, f^(-1)(y)={x in X:f(x)=y}. For instance, let X and Y be the complex numbers C. When f(z)=z^2, every ...

A Pascal's triangle written in a square grid and padded with zeros, as written by Jakob Bernoulli (Smith 1984). The figurate number triangle therefore has entries a_(ij)=(i; ...