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Their values can be computed only with iterative techniques which are characterised by high computational complexity.
We present a variant of the classical integration by parts to introduce a new type of Taylor series expansion and to present some closed forms for integrals involving Jacobi and Laguerre polynomials, which cannot be directly obtained by usual symbolic computation programs, i.e., only some very specific values can be computed by the mentioned programs.
Parallel two-step W-methods are linearly-implicit integration methods where the s stage values can be computed in parallel.
Updating vectors and residual values can be computed as Algorithm 1, for (k=1,ldots,frac{n}{2}).
Then, the BSP values can be computed considering as ETR the total rate of each traffic type.
The updated values can be computed inside confidence intervals that correspond to the lower contours of the CRE-based residual to minimize.
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Similarly, objective function value can be computed given both an upper threshold and a lower threshold.
For each RYB color, its approximated RGB value can be computed by a trilinear interpolation in the RYB color cube.
For large samples, the p-value can be computed by replacing the unknown correlation by the sample correlation, and the resulting test is quite satisfactory.
The resulting design has the good properties such as: its χ2 value can be computed exactly and the upper bound on the dependency among all design columns is under control.
A p value can be computed for each prediction as the degree of randomness of the observed city block distance [51] and therefore the probability that the corresponding query target association occurs at random.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com