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Seeks to obtain the best numerical estimate of an integral by picking optimal abscissas x_i at which to evaluate the function f(x). The fundamental theorem of Gaussian ...

The determinant G(f_1,f_2,...,f_n)=|intf_1^2dt intf_1f_2dt ... intf_1f_ndt; intf_2f_1dt intf_2^2dt ... intf_2f_ndt; | | ... |; intf_nf_1dt intf_nf_2dt ... intf_n^2dt|.

The study, first developed by Boole, of shift-invariant operators which are polynomials in the differential operator D^~. Heaviside calculus can be used to solve any ordinary ...

A formula for the number of Young tableaux associated with a given Ferrers diagram. In each box, write the sum of one plus the number of boxes horizontally to the right and ...

A number with a continued fraction whose terms are the values of one or more polynomials evaluated on consecutive integers and then interleaved. This property is preserved by ...

The polynomials in the diagonal of the Smith normal form or rational canonical form of a matrix are called its invariant factors.

An element a of a ring which is nonzero, not a unit, and whose only divisors are the trivial ones (i.e., the units and the products ua, where u is a unit). Equivalently, an ...

Let A be a matrix with the elementary divisors of its characteristic matrix expressed as powers of its irreducible polynomials in the field F[lambda], and consider an ...

Coefficients which appear in Lagrange interpolating polynomials where the points are equally spaced along the abscissa.

A polynomial is called logarithmically concave (or log-concave) if the sequence of its coefficients is logarithmically concave. If P(x) is log-convex and Q(x) is unimodal, ...