In statistics, Bessel's correction, named after Friedrich Bessel, is the use of n − 1 instead of n in the formula for the sample variance and sample standard deviation, where n is the number of observations in a sample: it corrects the bias in the estimation of the population variance, and some (but not all) of the bias in the estimation of the population standard deviation.
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It is especially useful for equations such as Bessel's equation where the solutions do not have a simple analytical form, because in such cases the Wronskian is difficult to compute directly.
In 2011, she was elected Fellow of the American Physical Society; and she won a Friedrich Wilhelm Bessel Research Award from the Alexander von Humboldt Foundation for developing robust electronic structure methods for open-shell and electronically excited species, and creative use of ab initio theory to understand the chemistry of bimolecules, reaction intermediates, and photoinduced processes.
This differential equation, and the Riccati–Bessel solutions, arises in the problem of scattering of electromagnetic waves by a sphere, known as Mie scattering after the first published solution by Mie (1908).
Johann Franz Bessel (in religion Gottfried) (b. 5 September 1672, at Buchen, in the Grand Duchy of Baden; d. at Göttweig, 22 January 1749) was a German Benedictine abbot and historian.