Sentence examples for this sum converges from inspiring English sources

Assuming again that each dollar is worth one utile, expected value of the Pasadena game is or This sum converges to $\ln 2 $; assuming that one dollar is worth one utile, this works out to about 69¢.

provided the sum converges.

where the sum converges absolutely and uniformly on compact subsets of the open unit disc.

The L-F CLT states that under certain regularity conditions the sum converges in distribution to a Gaussian random variable with mean and the variance as [24].

We define the atomic Hardy space (H^{p,q}_{L}(mathbb{C}^{n})) to be the set of all tempered distributions of the form (sum_{j} lambda_{j}a_{j}) (the sum converges in the topology of (mathcal{S}'(mathbb{C}^{n}))), where (a_{j}) are (H_{L}^{p,q} -atoms and (sum_{j}|lambda_{j}|^{p}<+infty).

Moreover, if Eλ denotes the orthogonal projection onto the eigenspace Hλ, then T = \sum_{\lambda\in\sigma(T)} \lambda E_\lambda, :where the sum converges with respect to the norm on B(H).

for those complex values of for which this infinite sum converges.

This paper presents necessary and sufficient conditions for a positive bounded operator on a separable Hilbert space to be the sum of a finite or infinite collection of projections (not necessarily mutually orthogonal), with the sum converging in the strong operator topology if the collection is infinite.

This decreased contribution of long sequences has the effect that the weighted sum converges to a limit.

provided sum converges absolutely.

where the previous sum converges in quadratic mean since |1−α i |<0 implies that (sum _{j=0}^{infty }| 1-alpha _{i})^{j}| 1-alpha{1}{alpha _{i}}< infty ).