Search Results for "Euler Maclaurin Integration Formulas"

The Euler-Mascheroni constant gamma=0.577215664901532860606512090082402431042... (OEIS A001620) was calculated to 16 digits by Euler in 1781 and to 32 decimal places by ...

Euler conjectured that at least n nth powers are required for n>2 to provide a sum that is itself an nth power. The conjecture was disproved by Lander and Parkin (1967) with ...

A differential k-form can be integrated on an n-dimensional manifold. The basic example is an n-form alpha in the open unit ball in R^n. Since alpha is a top-dimensional ...

Contour integration is the process of calculating the values of a contour integral around a given contour in the complex plane. As a result of a truly amazing property of ...

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...

Angle addition formulas express trigonometric functions of sums of angles alpha+/-beta in terms of functions of alpha and beta. The fundamental formulas of angle addition in ...

In order to integrate a function over a complicated domain D, Monte Carlo integration picks random points over some simple domain D^' which is a superset of D, checks whether ...

A beautiful approximation to the Euler-Mascheroni constant gamma is given by pi/(2e)=0.57786367... (1) (OEIS A086056; E. W. Weisstein, Apr. 18, 2006), which is good to three ...

Inverse function integration is an indefinite integration technique. While simple, it is an interesting application of integration by parts. If f and f^(-1) are inverses of ...

Euler's 6n+1 theorem states that every prime of the form 6n+1, (i.e., 7, 13, 19, 31, 37, 43, 61, 67, ..., which are also the primes of the form 3n+1; OEIS A002476) can be ...