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Let ||f|| be the supremum of |f(x)|, a real-valued function f defined on (0,infty). If f is twice differentiable and both f and f^('') are bounded, Landau (1913) showed that ...

Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...

For s>1, the Riemann zeta function is given by zeta(s) = sum_(n=1)^(infty)1/(n^s) (1) = product_(k=1)^(infty)1/(1-1/(p_k^s)), (2) where p_k is the kth prime. This is Euler's ...

The word "pole" is used prominently in a number of very different branches of mathematics. Perhaps the most important and widespread usage is to denote a singularity of a ...

The Cauchy principal value of a finite integral of a function f about a point c with a<=c<=b is given by ...

The conjugate gradient method is an algorithm for finding the nearest local minimum of a function of n variables which presupposes that the gradient of the function can be ...

The average distance between two points chosen at random inside a unit cube (the n=3 case of hypercube line picking), sometimes known as the Robbins constant, is Delta(3) = ...

A recurrence equation (also called a difference equation) is the discrete analog of a differential equation. A difference equation involves an integer function f(n) in a form ...

To pick a random point on the surface of a unit sphere, it is incorrect to select spherical coordinates theta and phi from uniform distributions theta in [0,2pi) and phi in ...

The Andrews-Gordon identity (Andrews 1974) is the analytic counterpart of Gordon's combinatorial generalization of the Rogers-Ramanujan identities (Gordon 1961). It has a ...