Sentence examples for computational formulae from inspiring English sources

In this paper we present two computational formulae for one kind of reciprocal sums related to the Riemann zeta-function at integer points (s=4,5), which answers an open problem proposed by Lin J. Inequall. Appl. 2016:32016016).

In this paper, we use the elementary method and the reciprocity theorem of Dedekind sums to study the computational problem of one kind Dedekind sums, and give two interesting computational formulae related to Dedekind sums and the second-order linear recurrence polynomials.

The main purpose of this paper is, using the properties of Gauss sums and the mean value theorem of Dirichlet L-functions, to study a hybrid mean value problem involving certain Hardy sums and Kloosterman sums and give two exact computational formulae for them.

The main purpose of this paper is, using the properties of Gauss sums and the mean square value theorem of Dirichlet L-functions, to study a hybrid mean value problem involving certain Hardy sums and Kloosterman sums and give two exact computational formulae.

The Pell-Lucas numbers Q n are defined by Q n + 2 = 2 Q n + 1 + Q n, where Q 0 = 2 and Q 1 = 2. Let α = 1 + 2 and β = 1 − 2. Then from the characteristic equations x 2 − 2 x − 1 = 0, we also have the computational formulae P n = 1 2 2 ( α n − β n ) and Q n = α n + β n.

We study their computational formulas and relationships.

The fitting computational formulas are applied in the mathematical model.

(2.1) These inequalities allow us to study the computational formulas of Theorem 1.

For integer (s=4), does there exist an exact computational formula for (1)?

Furthermore, for (a_{k}=k^{5}), we also have an analogous computational formula.

A computational formula of the new discrepancy is also given by the functional method.