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In elliptic cylindrical coordinates, the scale factors are h_u=h_v=sqrt(sinh^2u+sin^2v), h_z=1, and the separation functions are f_1(u)=f_2(v)=f_3(z)=1, giving a Stäckel ...

Let l(x) be an nth degree polynomial with zeros at x_1, ..., x_n. Then the fundamental Hermite interpolating polynomials of the first and second kinds are defined by ...

A synonym for analytic function, regular function, differentiable function, complex differentiable function, and holomorphic map (Krantz 1999, p. 16). The word derives from ...

A matrix whose entries are all integers. Special cases which arise frequently are those having only (-1,1) as entries (e.g., Hadamard matrix), (0,1)-matrices having only ...

A polynomial of the form f(x)=a_nx^n+a_(n-1)x^(n-1)+...+a_1x+a_0 having coefficients a_i that are all integers. An integer polynomial gives integer values for all integer ...

Integration under the integral sign is the use of the identity int_a^bdxint_(alpha_0)^alphaf(x,alpha)dalpha=int_(alpha_0)^alphadalphaint_a^bf(x,alpha)dx (1) to compute an ...

The tangent space at a point p in an abstract manifold M can be described without the use of embeddings or coordinate charts. The elements of the tangent space are called ...

Let S be a mathematical statement, then the Iverson bracket is defined by [S]={0 if S is false; 1 if S is true, (1) and corresponds to the so-called characteristic function. ...

An algorithm in control theory introduced by Kalman (1960) and refined by Kalman and Bucy (1961). It is an algorithm which makes optimal use of imprecise data on a linear (or ...

A theorem, also called the iteration theorem, that makes use of the lambda notation introduced by Church. Let phi_x^((k)) denote the recursive function of k variables with ...