Sentence examples for the complete sums from inspiring English sources

By applying their generating functions, they derived the complete sums of products of the twisted (h, q -extension of Euler polynomials and numbers.

In [1], Simsek evaluated the complete sums for the Euler numbers and polynomials and obtained some identities related to Euler numbers and polynomials from his complete sums, and Jang et al. [2] also considered the sums of products of Euler numbers.

Hence we have the complete sum for q-Euler polynomials as follows.

The complete "sum-over-trips" rules for the more general case of an arbitrary network geometry are also presented.

We have the formulae for the complete sum of the products of -Euler polynomials related to the higher order -Euler polynomials using the fermionic -adic -Volkenborn integral on.

In this paper, we will evaluate the complete sum of the -Euler polynomials and numbers using the fermionic -adic -Volkenborn integral on.

They should not be allowed in personal care products, even if they are natural substances  The chemical safety report does not need to consider the risks to human health from the use of cosmetic products ([20] Art. 14 5(b)) Realistic risk assessments should consider the complete sum of exposure routes.

Based on a half adder the constraints for a full adder can be derived as given in Formula 9. Variable S full is the complete sum of the two bits A and B, where the variable C2 is the resulting carry over.

By applying these generating functions, we prove complete sums of products of the twisted -extension of Euler polynomials and numbers.

This is a little stronger than the classical result of the complete Gauss sums in the case when ((n,q >1).

We use the abbreviation (sum_{mathbf{x}} = sum_{{mathbf{x}} inmathbb{Z}_{p^{2} }^{n} } ) for complete sums.