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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). ...

The Gudermannian function is the odd function denoted either gamma(x) or gd(x) which arises in the inverse equations for the Mercator projection. phi(y)=gd(y) expresses the ...

The principal branch of an analytic multivalued function, also called a principal sheet, is a single-valued "slice" (i.e., branch) of the function chosen that is for ...

The Jacobi polynomials, also known as hypergeometric polynomials, occur in the study of rotation groups and in the solution to the equations of motion of the symmetric top. ...

The two functions theta(x) and psi(x) defined below are known as the Chebyshev functions. The function theta(x) is defined by theta(x) = sum_(k=1)^(pi(x))lnp_k (1) = ...

A triangle center (sometimes simply called a center) is a point whose trilinear coordinates are defined in terms of the side lengths and angles of a triangle and for which a ...

If f is continuous on a closed interval [a,b], and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that ...

The q-analog of the binomial theorem (1-z)^n=1-nz+(n(n-1))/(1·2)z^2-(n(n-1)(n-2))/(1·2·3)z^3+... (1) is given by (1-z/(q^n))(1-z/(q^(n-1)))...(1-z/q) ...

A random-connection model (RCM) is a graph-theoretic model of continuum percolation theory characterized by the existence of a stationary point process X and a non-increasing ...

Let phi_x^((k)) denote the recursive function of k variables with Gödel number x, where (1) is normally omitted. Then if g is a partial recursive function, there exists an ...