WebGlaisher provided an asymptotic formula for the hyperfactorials, ... where is the Glaisher–Kinkelin constant. Other properties. According to an analogue of Wilson's theorem on the behavior of factorials modulo prime numbers, when is an odd prime number ) () / ()!! (), where !! is the notation for the double factorial. ... WebThe floor function \lfloor x \rfloor ⌊x⌋ is defined to be the greatest integer less than or equal to the real number x x. The fractional part function \ { x \} {x} is defined to be the difference between these two: Let x x be a real number. Then the fractional part of x x is. \ {x\}= x -\lfloor x \rfloor. {x} = x −⌊x⌋.
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WebEuler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma ... γ can also be expressed as follows where A is the Glaisher–Kinkelin constant: Web1, 1, 1, 9, 9, 30, 66, 106, 274, 459, 1010, 1862, 3552, 6973, 12446, 24245, 43041, 80372, 144482, 259633, 468047, 822642, 1468714, 2556542, 4493704, 7782441, 13470564 ...
WebMathematical functions in the Wolfram Language are given names according to definite rules. As with most Wolfram Language functions, the names are usually complete English words, fully spelled out. For a few very common functions, the Wolfram Language uses the traditional abbreviations. Thus the modulo function, for example, is Mod, not Modulo. Web(OEIS A086237), where is the Euler-Mascheroni constant, is the Riemann zeta function, and is the Glaisher-Kinkelin constant (Knuth 1998, p. 357). The notation is generally used for this constant (Knuth 1998, p. 357, Finch 2003, pp. 156-157), though other authors use (Ustinov 2010) or (Dimitrov et al. 2000).. The related constant originally considered by …
WebThe Glaisher-Kinkelin constant \(A = \exp(\frac{1}{12}-\zeta'(-1))\). EXAMPLES: sage: float ( glaisher ) 1.2824271291006226 sage: glaisher . n ( digits = 60 ) 1.28242712910062263687534256886979172776768892732500119206374 sage: a = glaisher + 2 sage: a glaisher + 2 sage: parent ( a ) Symbolic Ring WebM. Bresse (1867) computed 24 decimals of using a technique from E. Kummer's work. J. Glaisher (1877) evaluated 20 digits of the Catalan constant, which he extended to 32 digits in 1913. The Catalan constant is applied in number theory, combinatorics, and different areas of mathematical analysis.
WebMathematische Konstante. Eine mathematische Konstante ist eine wohldefinierte, reelle, nicht- ganzzahlige Zahl, die in der Mathematik von besonderem Interesse ist. [1] Anders als physikalische Konstanten werden mathematische Konstanten unabhängig von jedem physikalischen Maß definiert und sind demnach einheitenlos.
WebDec 24, 2012 · The Glaisher-Kinkelin constant , the constants and below introduced by Choi and Srivastava have been used, among other things, in the closed-form evaluation of certain series involving zeta functions and in calculation of some integrals of multiple Gamma functions. la jolla la hojaWebCatalan (or Glaisher) combinatorial constant. glaisher A. 1.28242 Decimal expansion of Glaisher-Kinkelin constant. khinchin k. 2.685452 Decimal expansion of Khinchin constant. extreme_value_skewness 12√6 ζ(3)/ π 3. 1.139547 la jolla laser visionWebFredrik Johansson et al., mpmath, Glaisher's constant to 20,000 digits. Hermann Kinkelin, Über eine mit der Gammafunction verwandte Transcendente und deren Anwendung auf die Integralrechnung, Journal für die reine und angewandte Mathematik, … la jolla lasik institutela jolla landslideWebMar 24, 2024 · where is the Euler-Mascheroni constant and is the Glaisher-Kinkelin constant. The derivative is given by (11) See also Barnes G-Function, Glaisher-Kinkelin Constant, K-Function, Superfactorial Explore with Wolfram Alpha. More things to try: 10 - 9 + 8 - 7 + 6 - 5 + 4 - 3 + 2 - 1; la jolla leopard sharksWebJun 20, 2016 · Finally, in Section 4, we present the second general asymptotic expansion (1.6) and further discuss its special cases. It can be found that the Glaisher–Kinkelin constant A and the hyperfactorial function H(n) play the same roles in (1.1) as the constant 2 π and the factorial function play in the Stirling formula 2 π = lim n → ∞ n! n n ... la jolla leopard sharks mapWebFeb 9, 2016 · In this paper, some new continued fraction approximations, inequalities and rates of convergence of Glaisher–Kinkelin’s and Bendersky–Adamchik’s constants are provided. To demonstrate the superiority of our new convergent sequences over the classical sequences and Mortici’s sequences, some numerical computations are also … la jolla lasik institute cost