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A coordinate system similar to toroidal coordinates but with fourth-degree instead of second-degree surfaces for constant mu so that the toroids of circular cross section are ...

A differential k-form can be integrated on an n-dimensional manifold. The basic example is an n-form alpha in the open unit ball in R^n. Since alpha is a top-dimensional ...

A diagram lemma which states that, given the above commutative diagram with exact rows, the following holds: 1. If alpha is surjective, and beta and delta are injective, then ...

Let n>=0 and alpha_1, alpha_2, ...be the positive roots of J_n(x)=0, where J_n(z) is a Bessel function of the first kind. An expansion of a function in the interval (0,1) in ...

Because the Legendre polynomials form a complete orthogonal system over the interval [-1,1] with respect to the weighting function w(x)=1, any function f(x) may be expanded ...

Finch (2010) gives an overview of known results for random Gaussian triangles. Let the vertices of a triangle in n dimensions be normal (normal) variates. The probability ...

Gauss's forward formula is f_p=f_0+pdelta_(1/2)+G_2delta_0^2+G_3delta_(1/2)^3+G_4delta_0^4+G_5delta_(1/2)^5+..., (1) for p in [0,1], where delta is the central difference and ...

Gauss's theorema egregium states that the Gaussian curvature of a surface embedded in three-space may be understood intrinsically to that surface. "Residents" of the surface ...

Gibrat's distribution is a continuous distribution in which the logarithm of a variable x has a normal distribution, P(x)=1/(xsqrt(2pi))e^(-(lnx)^2/2), (1) defined over the ...

Let a spherical triangle Delta have angles A, B, and C. Then the spherical excess is given by Delta=A+B+C-pi.