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The Feuerbach point X_(11) (center of the Feuerbach hyperbola) lies on the nine-point circle. The Feuerbach antipode is the antipode of this point on nine-point circle. It ...

A fractional clique of a graph G is a nonnegative real function on the vertices of G such that sum of the values on the vertices of any independent set is at most one. The ...

int_a^b(del f)·ds=f(b)-f(a), where del is the gradient, and the integral is a line integral. It is this relationship which makes the definition of a scalar potential function ...

The periphery of a graph G is the subgraph of G induced by vertices that have graph eccentricities equal to the graph diameter. The periphery of a connected graph may be ...

A G-space provides local notions of harmonic, hyperharmonic, and superharmonic functions. When there exists a nonconstant superharmonic function greater than 0, it is a ...

The hacovercosine, also known as the hacoversed cosine and cohavercosine, is a little-used trigonometric function defined by hacovercos(z) = covercosz (1) = 1/2(1+sinz), (2) ...

A necessary and sufficient condition that there should exist at least one nondecreasing function alpha(t) such that mu_n=int_(-infty)^inftyt^ndalpha(t) for n=0, 1, 2, ..., ...

J_n(z) = 1/(2pi)int_(-pi)^pie^(izcost)e^(in(t-pi/2))dt (1) = (i^(-n))/piint_0^pie^(izcost)cos(nt)dt (2) = 1/piint_0^picos(zsint-nt)dt (3) for n=0, 1, 2, ..., where J_n(z) is ...

A polygonal number of the form n(5n-3)/2. The first few are 1, 7, 18, 34, 55, 81, 112, ... (OEIS A000566). The generating function for the heptagonal numbers is ...

A pyramidal number of the form n(n+1)(5n-2)/6, The first few are 1, 8, 26, 60, 115, ... (OEIS A002413). The generating function for the heptagonal pyramidal numbers is ...