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A Lie group is called semisimple if its Lie algebra is semisimple. For example, the special linear group SL(n) and special orthogonal group SO(n) (over R or C) are ...

Given a ring R with identity, the special linear group SL_n(R) is the group of n×n matrices with elements in R and determinant 1. The special linear group SL_n(q), where q is ...

A second-order ordinary differential equation d/(dx)[p(x)(dy)/(dx)]+[lambdaw(x)-q(x)]y=0, where lambda is a constant and w(x) is a known function called either the density or ...

A symmetric function on n variables x_1, ..., x_n is a function that is unchanged by any permutation of its variables. In most contexts, the term "symmetric function" refers ...

The tangential circle of a reference triangle is the circumcircle of the tangential triangle. Its center is Kimberling center X_(26), which has center function ...

A triple of three arbitrary vectors with common vertex (Altshiller-Court 1979), often called a trihedral angle since it determines three planes. The vectors are often taken ...

The word weight has many uses in mathematics. It can refer to a function w(x) (also called a weighting function or weighting function) used to normalize orthogonal functions. ...

The de Longchamps circle is defined as the radical circle of the power circles of a given reference triangle. It is defined only for obtuse triangles. It is the complement of ...

There are several q-analogs of the cosine function. The two natural definitions of the q-cosine defined by Koekoek and Swarttouw (1998) are given by cos_q(z) = ...

The exponential function has two different natural q-extensions, denoted e_q(z) and E_q(z). They are defined by e_q(z) = sum_(n=0)^(infty)(z^n)/((q;q)_n) (1) = _1phi_0[0; ...