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Given F_1(x,y,z,u,v,w) = 0 (1) F_2(x,y,z,u,v,w) = 0 (2) F_3(x,y,z,u,v,w) = 0, (3) if the determinantof the Jacobian |JF(u,v,w)|=|(partial(F_1,F_2,F_3))/(partial(u,v,w))|!=0, ...

An infinitesimal is some quantity that is explicitly nonzero and yet smaller in absolute value than any real quantity. The understanding of infinitesimals was a major ...

A type of plot invented by M. Trott that shows the behavior of a function near and far from the origin simultaneously. Inside a given radius, the plot shows the actual value ...

The finite Fourier cosine transform of an apodization function, also known as an apparatus function. The instrument function I(k) corresponding to a given apodization ...

Given a smooth function f:R^n->R^n, if the Jacobian is invertible at 0, then there is a neighborhood U containing 0 such that f:U->f(U) is a diffeomorphism. That is, there is ...

The substitution of re^(itheta) for z in a polynomial p(z). p(z) is then plotted as a function of theta for a given r in the complex plane. By varying r so that the curve ...

Applying the Kaprekar routine to 4-digit number reaches 0 for exactly 77 4-digit numbers, while the remainder give 6174 in at most 8 iterations. The value 6174 is sometimes ...

A function that has a natural boundary.

Laplace's integral is one of the following integral representations of the Legendre polynomial P_n(x), P_n(x) = 1/piint_0^pi(du)/((x+sqrt(x^2-1)cosu)^(n+1))du (1) = ...

A discrete distribution of a random variable such that every possible value can be represented in the form a+bn, where a,b!=0 and n is an integer.