Sentence examples for a closed formula from inspiring English sources

Gödel's incompleteness theorem, generalized likewise, says that, in the usual language of arithmetic, it is not enough to look only at ω-complete models: Assuming that ℒ is consistent and that the theorems of ℒ are recursively enumerable, with the help of a decidable notion of proof, there is a closed formula g in ℒ, which is true in every ω-complete model, yet g is not a theorem in ℒ.

A sentence is a closed formula of the language.

In 2009, Koch presented a closed formula for an ASD posterior [2].

We provide a closed formula for the superpolynomial, which confirms the slice invariance when the Hopf link is colored with totally anti-symmetric representations.

It is determined by applying a closed formula that was obtained by the first author and involves the characteristic polynomial of the modal differential equation.

We derive a closed formula for the probability that each vehicle in the network has at least k neighbors (k=1,2,3,⋯).

This is done by using an explicit closed formula for the Vandermonde matrix inverse.

Present the closed formula for an as a polynomial with known coefficients.

The solvability of (25) along with (27) shows that for ((a_{k})_{kge-2}) we can find a closed form formula, from which along with (29) the formulas for (y_{k}) can also be obtained, as described above.

The solvability of (25) shows that for ((a_{k})_{kge-2}) can be found a closed form formula. Therefore, using equation (29) and known formulas for the following sums: begin{aligned} s_{m}^{(j)} zeta)=sum_{k=1}^{m}k^{j} zeta^{k}, quad min {mathbb {N}}_{0}, end{aligned} (30) where (j=overline {0,2}) (see, e.g., [31, 33]), the closed form formula for ((y_{k})_{kin {mathbb {N}}}) is easily obtained.

Employing such obtained formulas for (a_{k}) and (y_{k}) in (25), we obtain a closed form formula for the solution to (15).