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Clairaut's difference equation is a special case of Lagrange's equation (Sokolnikoff and Redheffer 1958) defined by u_k=kDeltau_k+F(Deltau_k), (1) or in "x notation," ...

A set S is discrete in a larger topological space X if every point x in S has a neighborhood U such that S intersection U={x}. The points of S are then said to be isolated ...

For a particular format in the IEEE 754-2008 framework, a normal number is a finite nonzero floating-point number with magnitude greater than or equal to a minimum value ...

Let f be an entire function of finite order lambda and {a_j} the zeros of f, listed with multiplicity, then the rank p of f is defined as the least positive integer such that ...

A list of five properties of a topological space X expressing how rich the "population" of open sets is. More precisely, each of them tells us how tightly a closed subset can ...

The Goh-Schmutz constant is defined by the integrals C = int_0^infty(ln(1+t))/(e^t-1)dt (1) = int_0^inftyln[1-ln(1-e^(-t))]dt (2) = ...

If x takes only nonnegative values, then P(x>=a)<=(<x>)/a. (1) To prove the theorem, write <x> = int_0^inftyxP(x)dx (2) = int_0^axP(x)dx+int_a^inftyxP(x)dx. (3) Since P(x) is ...

A q-analog of the beta function B(a,b) = int_0^1t^(a-1)(1-t)^(b-1)dt (1) = (Gamma(a)Gamma(b))/(Gamma(a+b)), (2) where Gamma(z) is a gamma function, is given by B_q(a,b) = ...

The mean triangle area of a triangle picked inside a regular n-gon of unit area is A^__n=(9cos^2omega+52cosomega+44)/(36n^2sin^2omega), (1) where omega=2pi/n (Alikoski 1939; ...

The structure constant is defined as iepsilon_(ijk), where epsilon_(ijk) is the permutation symbol. The structure constant forms the starting point for the development of Lie ...