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Let a discrete distribution have probability function p_k, and let a second discrete distribution have probability function q_k. Then the relative entropy of p with respect ...

There are two sets of constants that are commonly known as Lebesgue constants. The first is related to approximation of function via Fourier series, which the other arises in ...

The series sum_(k=1)^infty1/k (1) is called the harmonic series. It can be shown to diverge using the integral test by comparison with the function 1/x. The divergence, ...

A related rates problem is the determination of the rate at which a function defined in terms of other functions changes. Related rates problems can be solved by computing ...

A geometric series sum_(k)a_k is a series for which the ratio of each two consecutive terms a_(k+1)/a_k is a constant function of the summation index k. The more general case ...

Given a positive nondecreasing sequence 0<lambda_1<=lambda_2<=..., the zeta-regularized product is defined by product_(n=1)^^^inftylambda_n=exp(-zeta_lambda^'(0)), where ...

The Gram series is an approximation to the prime counting function given by G(x)=1+sum_(k=1)^infty((lnx)^k)/(kk!zeta(k+1)), (1) where zeta(z) is the Riemann zeta function ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

A lattice polygon formed by a three-choice walk. The anisotropic perimeter and area generating function G(x,y,q)=sum_(m>=1)sum_(n>=1)sum_(a>=a)C(m,n,a)x^my^nq^a, where ...

If a function analytic at the origin has no singularities other than poles for finite x, and if we can choose a sequence of contours C_m about z=0 tending to infinity such ...