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Let A be a normed (Banach) algebra. An algebraic left A-module X is said to be a normed (Banach) left A-module if X is a normed (Banach) space and the outer multiplication is ...

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. ...

Simplemindedly, a number theoretic transform is a generalization of a fast Fourier transform obtained by replacing e^(-2piik/N) with an nth primitive root of unity. This ...

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 ...

The wave equation in oblate spheroidal coordinates is del ^2Phi+k^2Phi=partial/(partialxi_1)[(xi_1^2+1)(partialPhi)/(partialxi_1)] ...

A univariate function f(x) is said to be odd provided that f(-x)=-f(x). Geometrically, such functions are symmetric about the origin. Examples of odd functions include x, ...

In the equianharmonic case of the Weierstrass elliptic function, corresponding to invariants g_2=0 and g_3=1, the corresponding real half-period is given by omega_2 = ...

The omega constant is defined as W(1)=0.5671432904... (1) (OEIS A030178), where W(x) is the Lambert W-function. It is available in the Wolfram Language using the function ...

Several flavors of the open mapping theorem state: 1. A continuous surjective linear mapping between Banach spaces is an open map. 2. A nonconstant analytic function on a ...

The operator norm of a linear operator T:V->W is the largest value by which T stretches an element of V, ||T||=sup_(||v||=1)||T(v)||. (1) It is necessary for V and W to be ...