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The score function u(theta) is the partial derivativeof the log-likelihood function F(theta)=lnL(theta), where L(theta) is the standard likelihood function. Defining the ...

Let p run over all distinct primitive ordered periodic geodesics, and let tau(p) denote the positive length of p, then every even function h(rho) analytic in ...

The shah function is defined by m(x) = sum_(n=-infty)^(infty)delta(x-n) (1) = sum_(n=-infty)^(infty)delta(x+n), (2) where delta(x) is the delta function, so m(x)=0 for x not ...

Borwein et al. (2004, pp. 4 and 44) term the expression of the integrals I_1 = int_0^1x^xdx (1) = 0.783430510... (2) I_2 = int_0^1(dx)/(x^x) (3) = 1.291285997... (4) (OEIS ...

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 ...

A weakly binary tree is a planted tree in which all nonroot graph vertices are adjacent to at most three graph vertices. Let g(z)=sum_(i=0)^inftyg_iz^i, (1) be the generating ...

Suppose W is the set of all complex-valued functions f on the interval [0,2pi] of the form f(t)=sum_(k=-infty)^inftyalpha_ke^(ikt) (1) for t in [0,2pi], where the alpha_k in ...

The beta function B(p,q) is the name used by Legendre and Whittaker and Watson (1990) for the beta integral (also called the Eulerian integral of the first kind). It is ...

Given an n-ball B^n of radius R, find the distribution of the lengths s of the lines determined by two points chosen at random within the ball. The probability distribution ...

A general type of statistical distribution which is related to the gamma distribution. Beta distributions have two free parameters, which are labeled according to one of two ...