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The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

The n-dimensional Keller graph, sometimes denoted G_n (e.g., Debroni et al. 2011), can be defined on a vertex set of 4^n elements (m_1,...,m_n) where each m_i is 0, 1, 2, or ...

LCF notation is a concise and convenient notation devised by Joshua Lederberg (winner of the 1958 Nobel Prize in Physiology and Medicine) for the representation of cubic ...

The Mathieu functions are the solutions to the Mathieu differential equation (d^2V)/(dv^2)+[a-2qcos(2v)]V=0. (1) Even solutions are denoted C(a,q,v) and odd solutions by ...

Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...

A plane is a two-dimensional doubly ruled surface spanned by two linearly independent vectors. The generalization of the plane to higher dimensions is called a hyperplane. ...

A superellipse is a curve with Cartesian equation |x/a|^r+|y/b|^r=1, (1) first discussed in 1818 by Lamé. A superellipse may be described parametrically by x = acos^(2/r)t ...

A vector is formally defined as an element of a vector space. In the commonly encountered vector space R^n (i.e., Euclidean n-space), a vector is given by n coordinates and ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...