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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 ...

Consider the characteristic equation |lambdaI-A|=lambda^n+b_1lambda^(n-1)+...+b_(n-1)lambda+b_n=0 (1) determining the n eigenvalues lambda of a real n×n square matrix A, ...

Let s_1, s_2, ... be an infinite series of real numbers lying between 0 and 1. Then corresponding to any arbitrarily large K, there exists a positive integer n and two ...

Expanding the Riemann zeta function about z=1 gives zeta(z)=1/(z-1)+sum_(n=0)^infty((-1)^n)/(n!)gamma_n(z-1)^n (1) (Havil 2003, p. 118), where the constants ...

It is always possible to write a sum of sinusoidal functions f(theta)=acostheta+bsintheta (1) as a single sinusoid the form f(theta)=ccos(theta+delta). (2) This can be done ...

A theorem sometimes called "Euclid's first theorem" or Euclid's principle states that if p is a prime and p|ab, then p|a or p|b (where | means divides). A corollary is that ...

If {a_0,a_1,...} is a recursive sequence, then the set of all k such that a_k=0 is the union of a finite (possibly empty) set and a finite number (possibly zero) of full ...

For a smooth harmonic map u:M->N, where del is the gradient, Ric is the Ricci curvature tensor, and Riem is the Riemann tensor.

A tensor notation which considers the Riemann tensor R_(lambdamunukappa) as a matrix R_((lambdamu)(nukappa)) with indices lambdamu and nukappa.

The Poisson sum formula is a special case of the general result sum_(-infty)^inftyf(x+n)=sum_(k=-infty)^inftye^(2piikx)int_(-infty)^inftyf(x^')e^(-2piikx^')dx^' (1) with x=0, ...