Sentence examples for a partial sum of from inspiring English sources

We define the function S k which is a partial sum of f ∈ A by S k ( z ) = z + ( a k k ) z k, k ≥ 2, a k ≠ 0. (2).

In such a case, the solution can be found approximately as a partial sum of the series, (u_{n} overline{x},t)=sum_{k=0}^{n}f _{k} overline{x}) t^{alpha k}) in some reasonable interval of t, and thus the overall errors can be made smaller by adding more new terms as shown in the following case.

Finally, in practice one wants to approximate the function with a finite number of terms, let's say with a Taylor polynomial or a partial sum of the trigonometric series, respectively.

Each such value is exactly S z, j) plus a partial sum of the values in v g.

The C3 algorithm also uses a two-day guard band, but calculates a partial sum for the last three days of the positive deviation of the current value from the mean [ 6].

In this paper, we investigate the asymptotical behavior for a partial sum sequence of independent random variables, and we derive a law of the iterated logarithm type.

In the k-mer counting example, the combiner emits a partial sum from the subset of 1s it evaluates, and the reduce function sums over the list of partial sums.

For a function f ( z ) ∈ A, we introduce the partial sum of f ( z ) by f k ( z ) = z + ∑ n = 2 k a n z n, z ∈ U. (1).

In Section 2, we study order of approximation of a function by the n th Fourier series partial sum of a Hankel matrix transform.

Proposition 2 of Newman and Wright [3] shows that the partial sum of a sequence of mean zero associated random variables is a demimartingale.

Newman and Wright [2] extended Doob's maximal inequality and upcrossing inequality to the case of demimartingales, and pointed out that the partial sum of a sequence of mean zero associated random variables is a demimartingale.