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Let Xi be the xi-function defined by Xi(iz)=1/2(z^2-1/4)pi^(-z/2-1/4)Gamma(1/2z+1/4)zeta(z+1/2). (1) Xi(z/2)/8 can be viewed as the Fourier transform of the signal ...

The simple process of voting leads to surprisingly counterintuitive paradoxes. For example, if three people vote for three candidates, giving the rankings A, B, C; B, C, A; ...

The spherical harmonics form a complete orthogonal system, so an arbitrary real function f(theta,phi) can be expanded in terms of complex spherical harmonics by ...

The Hartley Transform is an integral transform which shares some features with the Fourier transform, but which, in the most common convention, multiplies the integral kernel ...

Vector addition is the operation of adding two or more vectors together into a vector sum. The so-called parallelogram law gives the rule for vector addition of two or more ...

If f(omega) is square integrable over the real omega-axis, then any one of the following implies the other two: 1. The Fourier transform F(t)=F_omega[f(omega)](t) is 0 for ...

The Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly ...

Let F(nu) and G(nu) be the Fourier transforms of f(t) and g(t), respectively. Then int_(-infty)^inftyf(t)g^_(t)dt ...

Specifying two angles A and B and a side a opposite A uniquely determines a triangle with area K = (a^2sinBsinC)/(2sinA) (1) = (a^2sinBsin(pi-A-B))/(2sinA). (2) The third ...

Exponential decay is the decrease in a quantity N according to the law N(t)=N_0e^(-lambdat) (1) for a parameter t and constant lambda (known as the decay constant), where e^x ...