Gamma: Exploring Euler's Constant

Euler's constant (sometimes also called the Euler–Mascheroni constant) is a mathematical constant usually denoted by the lowercase Greek letter gamma (γ).. It is defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by : = → (⁡ + =) = (+ ⌊ ⌋). Here, ⌊ ⌋ represents the floor function. The numerical value of Euler's constant, to 50 ...
17/12/2021 · The series sum_(k=1)^infty1/k (1) is called the harmonic series. It can be shown to diverge using the integral test by comparison with the function 1/x. The divergence, however, is very slow. Divergence of the harmonic series was first demonstrated by Nicole d'Oresme (ca. 1323-1382), but was mislaid for several centuries (Havil 2003, p. 23; Derbyshire 2004, pp. 9-10).
17/12/2021 · There are two kinds of power sums commonly considered. The first is the sum of pth powers of a set of n variables x_k, S_p(x_1,...,x_n)=sum_(k=1)^nx_k^p, (1) and the second is the special case x_k=k, i.e., S_p(n)=sum_(k=1)^nk^p. (2) General power sums arise commonly in statistics. For example, k-statistics are most commonly defined in terms of power sums.
Havil, Julian (2009-07-06), Gamma: Exploring Euler's Constant, Princeton Science Library (Paperback ed.), Princeton University Press, ISBN 978-0-691-14133-6, Julian Havil『オイラーの定数ガンマ γで旅する数学の世界』新妻弘監訳、共立出版、2009年5月25日。

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