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The polylogarithm Li_n(z), also known as the Jonquière's function, is the function Li_n(z)=sum_(k=1)^infty(z^k)/(k^n) (1) defined in the complex plane over the open unit ...

A Ruth-Aaron pair is a pair of consecutive numbers (n,n+1) such that the sums of the prime factors of n and n+1 are equal. They are so named because they were inspired by the ...

The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

The prime counting function is the function pi(x) giving the number of primes less than or equal to a given number x (Shanks 1993, p. 15). For example, there are no primes ...

Let z=re^(itheta)=x+iy be a complex number, then inequality |(zexp(sqrt(1-z^2)))/(1+sqrt(1-z^2))|<=1 (1) holds in the lens-shaped region illustrated above. Written explicitly ...

A square which can be dissected into a number of smaller squares with no two equal is called a perfect square dissection (or a squared square). Square dissections in which ...

A Pisot number is a positive algebraic integer greater than 1 all of whose conjugate elements have absolute value less than 1. A real quadratic algebraic integer greater than ...

A polyomino is a generalization of the domino to a collection of n squares of equal size arranged with coincident sides. Polyominos were originally called "super-dominoes" by ...

The radical line, also called the radical axis, is the locus of points of equal circle power with respect to two nonconcentric circles. By the chordal theorem, it is ...

The rectilinear crossing number of a graph G is the minimum number of crossings in a straight line embedding of G in a plane. It is variously denoted rcr(G), cr^_(G) ...