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If at least one of d, e, or f has the form q^(-N) for some nonnegative integer N (in which case both sums terminate after N+1 terms), then ...

Algebra

An Eisenstein series with half-period ratio tau and index r is defined by G_r(tau)=sum^'_(m=-infty)^inftysum^'_(n=-infty)^infty1/((m+ntau)^r), (1) where the sum sum^(') ...

The Mertens constant B_1, also known as the Hadamard-de la Vallee-Poussin constant, prime reciprocal constant (Bach and Shallit 1996, p. 234), or Kronecker's constant ...

Finch (2010) gives an overview of known results for random Gaussian triangles. Let the vertices of a triangle in n dimensions be normal (normal) variates. The probability ...

Likelihood is the hypothetical probability that an event that has already occurred would yield a specific outcome. The concept differs from that of a probability in that a ...

Given a sample of n variates X_1, ..., X_N, reorder them so that Y_1<Y_2<...<Y_N. Then Y_i is called the ith order statistic (Hogg and Craig 1970, p. 146), sometimes also ...

A statistical distribution published by William Gosset in 1908. His employer, Guinness Breweries, required him to publish under a pseudonym, so he chose "Student." Given N ...

The elliptic logarithm is generalization of integrals of the form int_infty^x(dt)/(sqrt(t^2+at)), for a real, which can be expressed in terms of logarithmic and inverse ...

For the hyperbolic partial differential equation u_(xy) = F(x,y,u,p,q) (1) p = u_x (2) q = u_y (3) on a domain Omega, Goursat's problem asks to find a solution u(x,y) of (3) ...