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Ewald summation, named after Paul Peter Ewald, is a method for computing long-range interactions (e.g. electrostatic interactions) in periodic systems. It was first developed as the method for calculating the electrostatic energies of ionic crystals, and is now commonly used for calculating long-range interactions in computational chemistry.
Definition. Given a series. define. If the limit. exists for some k, this is called the Hölder sum, or the ( H, k) sum, of the series. Particularly, since the Cesàro sum of a convergent series always exists, the Hölder sum of a series (that is Hölder summable) can be written in the following form:
Define the transform of by. Then the Mittag-Leffler sum of y is given by. if each sum converges and the limit exists. A closely related summation method, also called Mittag-Leffler summation, is given as follows ( Sansone & Gerretsen 1960 ). Suppose that the Borel transform converges to an analytic function near 0 that can be analytically ...
総和. この項目では、数学用語について説明しています。. 茨城県にあった自治体については「 総和町 」をご覧ください。. 数学 において、 総和 （ そうわ 、 summation ）とは、与えられた複数の数を全て足した 和 のことである。. 与えられた数たちの間に和 ...
A metric tensor is a (symmetric) (0, 2)-tensor; it is thus possible to contract an upper index of a tensor with one of the lower indices of the metric tensor in the product. This produces a new tensor with the same index structure as the previous tensor, but with lower index generally shown in the same position of the contracted upper index.
The other commonly formulated generalization of Cesàro summation is the sequence of (C, n) methods. It has been proven that (C, n) summation and (H, n) summation always give the same results, but they have different historical backgrounds. In 1887, Cesàro came close to stating the definition of (C, n) summation, but he gave only a few examples.
The hypergeometric differential equation. The hypergeometric function is a solution of Euler's hypergeometric differential equation. which has three regular singular points: 0,1 and ∞. The generalization of this equation to three arbitrary regular singular points is given by Riemann's differential equation.
