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Note
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72249105197
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Stirling numbers, introduced by Stirling (Ref.) in 1730, have been studied in the past by many celebrated mathematicians. Among them are Euler, Lagrange, Laplace, and Cauchy. Stirling numbers play an important role in combinatorics, number theory, probability, and statistics. There are two common sets of Stirling numbers, they are the so-called Stirling numbers of the first kind and Stirling numbers of the second kind (for details, see Refs.).
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72249093267
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Note
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μ2-were first obtained by Laskin [see Eqs. (26) and (27) in Ref.]. The second order moment defined by Eq. can be presented as Eq. (27) of Ref. if we take into account the well-known equations for the gamma function (μ), (μ+1) =μ (μ), and (2μ) = 22μ-1 /π (μ) (μ+ 1 2).
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22
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84887221515
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from MathWorld-A Wolfram Web Resource.
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