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A polyare is a polyform formed from a polyomino by removing of half of each square such that at least half of the original join between squares is retained. The first few ...

A simple polyhedron, also called a simplicial polyhedron, is a polyhedron that is topologically equivalent to a sphere (i.e., if it were inflated, it would produce a sphere) ...

A figurate number of the form StOct_n = O_n+8Te_(n-1) (1) = n(2n^2-1), (2) where O_n is an octahedral number and Te_n is a tetrahedral number. The first few are 1, 14, 51, ...

An alternating multilinear form on a real vector space V is a multilinear form F:V tensor ... tensor V->R (1) such that ...

Let the nth composition of a function f(x) be denoted f^((n))(x), such that f^((0))(x)=x and f^((1))(x)=f(x). Denote the composition of f and g by f degreesg(x)=f(g(x)), and ...

The Buchstab function omega(u) is defined by the delay differential equation {uomega(u)=1 for 1<=u<=2; (uomega(u))^'=omega(u-1) for u>2 (1) (Panario 1998). It approaches the ...

The catacaustic of a cardioid for a radiant point along the x-axis is complicated function of x. For x=0 (i.e., with radiant point at the cusp), however, the catacaustic for ...

A figurate number of the form, CCub_n=n^3+(n-1)^3=(2n-1)(n^2-n+1). The first few are 1, 9, 35, 91, 189, 341, ... (OEIS A005898). The generating function for the centered cube ...

Let {p_n(x)} be orthogonal polynomials associated with the distribution dalpha(x) on the interval [a,b]. Also let rho=c(x-x_1)(x-x_2)...(x-x_l) (for c!=0) be a polynomial of ...

The W-polynomials obtained by setting p(x)=3x and q(x)=-2 in the Lucas polynomial sequence. The first few Fermat polynomials are F_1(x) = 1 (1) F_2(x) = 3x (2) F_3(x) = ...