Sentence examples for double sum from inspiring English sources

Reversing the double sum of (A.11) and using [10, equation (8.352.4 ], we obtain (A.2).

Each term of the double sum of Eq. 10 corresponds to a different degree n k, where n k is a real number.

When the number of earthquakes is very large, the computing takes substantially long time due to the double sum in the first term of the log likelihood (8).

It reads (11 with (12)where δ denotes Dirac's delta function, e r, e ϑ and e φ are unit vectors of the spherical coordinate system, and is a short expression for the double sum in Eq. (9).

This observation encourages one to limit computations of the double sum in Equation 14 only to the neighborhood N i) of node i and yet get a potentially close approximation of the precise value of partial derivatives.

If the linearization formula of (P_n(x)) is available then we can compute (A_{i,j}) coefficients in Eq. (3) by using one sum instead of using double sum in Eq. (4).

replacing double limits of independent double sums by single limit of dependent double sums.  .

replacing rectangular area by triangular one; replacing double limits of independent double sums by single limit of dependent double sums.

This triangular double integral is defined by single limit of double sums of triangularly divided areas.

Note that in practice, the double sums in Equations 3 and 4 are finite.

The antisymmetric double integral here introduced demands only single limit of double sums of triangularly divided areas.