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An unsolved problem in mathematics attributed to Lehmer (1933) that concerns the minimum Mahler measure M_1(P) for a univariate polynomial P(x) that is not a product of ...

The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is ...

Roughly speaking, a tangent vector is an infinitesimal displacement at a specific point on a manifold. The set of tangent vectors at a point P forms a vector space called the ...

The Meijer G-function is a very general function which reduces to simpler special functions in many common cases. The Meijer G-function is defined by (1) where Gamma(s) is ...

The Motzkin numbers enumerate various combinatorial objects. Donaghey and Shapiro (1977) give 14 different manifestations of these numbers. In particular, they give the ...

The nearest integer function, also called nint or the round function, is defined such that nint(x) is the integer closest to x. While the notation |_x] is sometimes used to ...

For every dimension n>0, the orthogonal group O(n) is the group of n×n orthogonal matrices. These matrices form a group because they are closed under multiplication and ...

The Poincaré hyperbolic disk is a two-dimensional space having hyperbolic geometry defined as the disk {x in R^2:|x|<1}, with hyperbolic metric ...

P is the point on the line AB such that PA^_/PB^_=1. It can also be thought of as the point of intersection of two parallel lines. In 1639, Desargues (1864) became the first ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...