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The circle method is a method employed by Hardy, Ramanujan, and Littlewood to solve many asymptotic problems in additive number theory, particularly in deriving an asymptotic ...

A Gaussian quadrature-like formula for numerical estimation of integrals. It requires m+1 points and fits all polynomials to degree 2m, so it effectively fits exactly all ...

A quadrilateral which has an incircle, i.e., one for which a single circle can be constructed which is tangent to all four sides. Opposite sides of such a quadrilateral ...

pi may be computed using a number of iterative algorithms. The best known such algorithms are the Archimedes algorithm, which was derived by Pfaff in 1800, and the ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_7=f(x_7). Then Hardy's rule approximating the ...

Let I be a set, and let U be an ultrafilter on I, let phi be a formula of a given language L, and let {A_i:i in I} be any collection of structures which is indexed by the set ...

There are at least two meanings of the term "total derivative" in mathematics. The first is as an alternate term for the convective derivative. The total derivative is the ...

A method of numerically integrating ordinary differential equations by using a trial step at the midpoint of an interval to cancel out lower-order error terms. The ...

A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form f(x)=a_3x^3+a_2x^2+a_1x+a_0. An equation involving a cubic polynomial is called a ...

The Euler-Maclaurin integration and sums formulas can be derived from Darboux's formula by substituting the Bernoulli polynomial B_n(t) in for the function phi(t). ...