Further, Kim and Hu [24] obtained the closed formula of sums of products of any number of Apostol-Bernoulli numbers by expressing the sums of products of the Apostol-Bernoulli polynomials in terms of the special values of multiple Hurwitz-Lerch zeta functions at non-positive integers.
This allows us to express the sum of these series in terms of the considered trigonometric sums, and permits us to find sharp inequalities bounding these trigonometric sums.
At the same time, the function G expresses the sum of the squares of the deviations for all values over an hour, while the function A is calculated for one baseline value per hour.
Despite "This Land" later devolving into a bland patriotic staple, the song's full set of lyrics express the sum of Woody's philosophy about the good of the common people, the need to flatten out the economy so while the rich may still get the most, the poor get more than just some.
We define a function F that expresses the sum of probabilities of tables T with probability less than or equal to that of the table T, i.e. the P-value of T, as the sum of probabilities of multiple 2 × (k − 1) contingency tables: where r′ = min(r k, A).
The percent of the total variance in π accounted for by each main effect and the interaction was estimated by expressing the sequential sum of squares as a percentage of the total sum of squares.
For genes associated with multiple expressed signatures, the sum of abundance for all expressed signatures, including the signatures with more than one hit to the Arabidopsis genome, was used to indicate the abundance of each transcript in the sample.
As is known, when expressed in dB, the instantaneous path loss can be expressed as the sum of the mean path loss, the shadow fading, and the small-scale fading as follows PL d) = L d) + {X_{sigma}} + F (4).
Also, it is easy to show that any element in Y is uniquely expressed as the sum of an element KerL and an element from ImL.
In 1638 Fermat asserted that every whole number can be expressed as the sum of four or fewer squares.
