Ads
related to: summation calculator
Search results
Results from the WOW.Com Content Network
The next expression states equivalently that the variance of the sum is the sum of the diagonal of covariance matrix plus two times the sum of its upper triangular elements (or its lower triangular elements); this emphasizes that the covariance matrix is symmetric. This formula is used in the theory of Cronbach's alpha in classical test theory.
The geometric series + + + + … is an infinite series derived from a special type of sequence called a geometric progression, which is defined by just two parameters: the initial term and the common ratio .
The British flag theorem for rectangles equates two sums of two squares; The parallelogram law equates the sum of the squares of the four sides to the sum of the squares of the diagonals; Descartes' theorem for four kissing circles involves sums of squares; The sum of the squares of the edges of a rectangular cuboid equals the square of any ...
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.
The formula is a special case of the Euler–Boole summation formula for alternating series, providing yet another example of a convergence acceleration technique that can be applied to the Leibniz series. In 1992, Jonathan Borwein and Mark Limber used the first thousand Euler numbers to calculate π to 5,263 decimal places with the Leibniz ...
An important property of three-phase power is that the instantaneous power available to a resistive load, = =, is constant at all times.Indeed, let = = To simplify the mathematics, we define a nondimensionalized power for intermediate calculations, =
The case originally considered by Carl Friedrich Gauss was the quadratic Gauss sum, for R the field of residues modulo a prime number p, and χ the Legendre symbol.In this case Gauss proved that G(χ) = p 1 ⁄ 2 or ip 1 ⁄ 2 for p congruent to 1 or 3 modulo 4 respectively (the quadratic Gauss sum can also be evaluated by Fourier analysis as well as by contour integration).
Frobenius inner product, the dot product of matrices considered as vectors, or, equivalently the sum of the entries of the Hadamard product; Hadamard product of two matrices of the same size, resulting in a matrix of the same size, which is the product entry-by-entry; Kronecker product or tensor product, the generalization to any size of the ...
Ads
related to: summation calculator