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- W2111788286 abstract "We study discrete functions on equidistant and non-equidistant infinitesimal grids. We consider its difference quotients of higher order and give conditions for their near-equality to the corresponding derivatives. Important tools are the formula of Faa di Bruno for higher order derivatives and a discrete version of it. As an application of such transitions from the discrete to the continuous we extend the DeMoivre-Laplace Theorem to higher order: n-th order difference quotients of the binomial probability distribution tend to the corresponding n-th order partial differential quotients of the Gaussian distribution." @default.
- W2111788286 created "2016-06-24" @default.
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- W2111788286 date "2013-01-01" @default.
- W2111788286 modified "2023-09-29" @default.
- W2111788286 title "Discretisations of higher order and the theorems of Faà di Bruno and DeMoivre-Laplace" @default.
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- W2111788286 doi "https://doi.org/10.4115/jla.2013.5.6" @default.
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