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In this article, the authors present two identities involving products of the Bernoulli numbers, provide four alternative proofs for these two identities, derive two closed-form formulas for the Bernoulli numbers in terms of central factorial numbers of the second kind, and supply simple proofs of series expansions of (hyperbolic) cosecant and cotangent functions.
The research aims to emphasise the relevance of the Design of Experiments (DOE) technique as a reliable method for ensuring efficient use of statistical methods in routine industrial processes. A case study approach with a deductive strategy was used to assess the effectiveness of different DOE methods to achieve the desired objectives. Screening, mid-resolution and high-resolution DOE methods helped...
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