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Numerical integration is the approximate computation of an integral using numerical techniques. The numerical computation of an integral is sometimes called quadrature. ...

T-integration, which stands for "tunable numerical integration," is a fast, accurate, and numerically stable numerical integration formula given by ...

Let alpha(x) be a monotone increasing function and define an interval I=(x_1,x_2). Then define the nonnegative function U(I)=alpha(x_2)-alpha(x_1). The Lebesgue integral with ...

Since the derivative of a constant is zero, any constant may be added to an indefinite integral (i.e., antiderivative) and will still correspond to the same integral. Another ...

Let E be a set of expressions representing real, single-valued partially defined functions of one real variable. Let E^* be the set of functions represented by expressions in ...

A powerful numerical integration technique which uses k refinements of the extended trapezoidal rule to remove error terms less than order O(N^(-2k)). The routine advocated ...

A discrete subset of R^s which is closed under addition and subtraction and which contains Z^s as a subset.

The Lebesgue covering dimension is an important dimension and one of the first dimensions investigated. It is defined in terms of covering sets, and is therefore also called ...

The Riemann-Lebesgue Lemma, sometimes also called Mercer's theorem, states that lim_(n->infty)int_a^bK(lambda,z)Csin(nz)dz=0 (1) for arbitrarily large C and "nice" ...

A problem related to the continuum hypothesis which was solved by Solovay (1970) using the inaccessible cardinals axiom. It has been proven by Shelah and Woodin (1990) that ...