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nu(x) = int_0^infty(x^tdt)/(Gamma(t+1)) (1) nu(x,alpha) = int_0^infty(x^(alpha+t)dt)/(Gamma(alpha+t+1)), (2) where Gamma(z) is the gamma function (Erdélyi et al. 1981, p. ...

Numerical differentiation is the process of finding the numerical value of a derivative of a given function at a given point. In general, numerical differentiation is more ...

In order to recover all Fourier components of a periodic waveform, it is necessary to use a sampling rate nu at least twice the highest waveform frequency. The Nyquist ...

Let T be a linear operator on a separable Hilbert space. The spectrum sigma(T) of T is the set of lambda such that (T-lambdaI) is not invertible on all of the Hilbert space, ...

The orthogonal complement of a subspace V of the vector space R^n is the set of vectors which are orthogonal to all elements of V. For example, the orthogonal complement of ...

An isoptic curve formed from the locus of tangents meeting at right angles. The orthoptic of a parabola is its conic section directrix. The orthoptic of a central conic was ...

Overdamped simple harmonic motion is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0, (1) in which beta^2-4omega_0^2>0. (2) Therefore ...

The placement of objects so that they touch in some specified manner, often inside a container with specified properties. For example, one could consider a sphere packing, ...

At the points where a line X cuts the sides of a triangle DeltaA_1A_2A_3, draw three perpendiculars to the sides, one through each point of intersection. The resulting three ...

The pedal circle with respect to a pedal point P of a triangle DeltaA_1A_2A_3 is the circumcircle of the pedal triangle DeltaP_1P_2P_3 with respect to P. Amazingly, the ...