Sentence examples for alternating sum from inspiring English sources

Section 2: We give many properties of the unification of the Bernstein-type polynomials: partition of unity, alternating sum, subdivision property.

Using functional equations, we give new derivations for the sum and alternating sum of the Bernstein basis functions and a formula for the monomials in terms of the Bernstein basis functions.

If N Ā1, Ā2, · · ·, Ān) is the number of objects possessing none of the properties A1, A2, · · ·, An, then this number can be computed as an alternating sum of sums involving the numbers of objects that possess the properties This is the principle of inclusion and exclusion expressed by Sylvester.

These results follow simply from Hopf's trace formula which states that the alternating sum of traces in homology is equal to the alternating sum of traces on the chains.

Note that Theorem 5.2 can be also obtained from the algebraic alternating sum formula applied to sequence (5.4).

Remark 3.3 Goldman [6], [[5], Chapter 5, pp.299-306] derived the formula for the alternating sum of the Bernstein basis functions algebraically.

In particular, the techniques for dealing with alternating sums can be applied to study other types of alternating sums, which will be presented in a future paper.

In this article, we focus ourselves on the sums and alternating sums of the products of two reciprocal Fibonacci numbers.

In this section, we extend the analysis of the sums of the products of two reciprocal Fibonacci numbers to alternating sums.

In this paper, we investigate the sums and alternating sums of the products of two reciprocal Fibonacci numbers in various ways.

By using these numbers and polynomials, he proved the -analogue of alternating sums of powers of consecutive integers due to Euler: (1.1).