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Expanding the Riemann zeta function about z=1 gives zeta(z)=1/(z-1)+sum_(n=0)^infty((-1)^n)/(n!)gamma_n(z-1)^n (1) (Havil 2003, p. 118), where the constants ...

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, ...

Roughly speaking, the metric tensor g_(ij) is a function which tells how to compute the distance between any two points in a given space. Its components can be viewed as ...

If a function phi:(0,infty)->(0,infty) satisfies 1. ln[phi(x)] is convex, 2. phi(x+1)=xphi(x) for all x>0, and 3. phi(1)=1, then phi(x) is the gamma function Gamma(x). ...

A quartic curve that resembles the symbol for the zodiacal sign Capricorn given by the implicit equation a^2x^2(x^2+y^2)-b(ay-x^2-y^2)^2=0, where a>0, b>a^2. The curve ...

Let V be a vector space over a field K, and let A be a nonempty set. For an appropriately defined affine space A, K is called the coefficient field.

Two cones placed apex to apex. The double cone is given by algebraic equation (z^2)/(c^2)=(x^2+y^2)/(a^2).

The mathematical study of a nonlinear equation f(phi)=y, where f maps from a Hilbert space X to a Hilbert space Y and y in Y which abstracts the construction of optical ...

Given a convex plane region with area A and perimeter p, then |N-A|<p, where N is the number of enclosed lattice points.

An integer which is expressible in more than one way in the form x^2+Dy^2 or x^2-Dy^2 where x^2 is relatively prime to Dy^2. If the integer is expressible in only one way, it ...