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According to Euler's rotation theorem, any rotation may be described using three angles. If the rotations are written in terms of rotation matrices D, C, and B, then a ...

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

A generating function f(x) is a formal power series f(x)=sum_(n=0)^inftya_nx^n (1) whose coefficients give the sequence {a_0,a_1,...}. The Wolfram Language command ...

The graph distance matrix, sometimes also called the all-pairs shortest path matrix, is the square matrix (d_(ij)) consisting of all graph distances from vertex v_i to vertex ...

Given a finitely generated Z-graded module M over a graded ring R (finitely generated over R_0, which is an Artinian local ring), the Hilbert function of M is the map ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...

Kepler's equation gives the relation between the polar coordinates of a celestial body (such as a planet) and the time elapsed from a given initial point. Kepler's equation ...

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 ...

The logarithmic spiral is a spiral whose polar equation is given by r=ae^(btheta), (1) where r is the distance from the origin, theta is the angle from the x-axis, and a and ...

A manifold is a topological space that is locally Euclidean (i.e., around every point, there is a neighborhood that is topologically the same as the open unit ball in R^n). ...