Sentence examples for close formulae from inspiring English sources

We now use Theorem 4.1 to obtain the following close formulae of sums of any positive powers for the ( p, q ) -Fibonacci and Lucas polynomials.

For another close formulae of sums of powers of the classical Fibonacci and Lucas numbers, one is referred to [13, 14].

In this section, we shall extend the two sum relations due to Lee and Asci and give the close formulae of sums of any positive powers for the ( p, q ) -Fibonacci and Lucas polynomials.

formula, then every close system satisfies a close formula.

We also show that the timed verification logic TCTL is robust with respect to our notion of quantitative bisimilarity, in particular, if a system satisfies a formula, then every close system satisfies a close formula.

We show that timed \CTL is robust with respect to our quantitative version of bisimilarity, in particular, if a system satisfies a formula, then every close system satisfies a close formula.

This paper derives a close formula of connectivity probability with interference and Nakagami-m fading which is never obtained in previous works.

A simple example when the projection has a close formula is the following.

Since there is no close formula for for we provide Algorithm Probability Computation for to express. is computed similar to with the exception that it depends on not only the probability of event occurrences but also their probability of detection.

Some closed formulae of sums of products of any number of Apostol-Bernoulli and Apostol-Euler polynomials and numbers are established by applying the generating function methods and some summation transform techniques.

March 10: l1x.pdf: Closed formulas for L 1,chi) and their relationship with cyclotomic units, class numbers, and the distribution of quadratic residues.