GeneralizationsThe Glaisher-Kinkelin constant can be viewed as the first constant in a sequence of infinitely many so-called generalized Glaisher constants or Bendersky constants. They emerge from studying the following product:… See more
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- Glaisher-Kinkelin constant · A1.2824271291The Glaisher-Kinkelin constant is a mathematical constant used in various sums and integrals, specifically those related to Gamma functions and Riemann zeta functions.
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See more science constantsNew content will be added above the current area of focus upon selectionSee fewer science constants Glaisher-Kinkelin Constant -- from Wolfram MathWorld
The Glaisher-Kinkelin constant A is defined by lim_(n->infty)(H(n))/(n^(n^2/2+n/2+1/12)e^(-n^2/4))=A (1) (Glaisher 1878, 1894, Voros 1987), where H(n) is the hyperfactorial, as well as lim_(n …
Glaisher constant: Introduction to the classical constants
Classical constants and the imaginary unit include eight basic constants: golden ratio , pi , the number of radians in one degree , Euler number (or Euler constant or base of natural …
Glaisher—Wolfram Language Documentation
Glaisher is the symbol representing Glaisher's constant , also known as the Glaisher – Kinkelin constant. Glaisher has a number of equivalent definitions throughout mathematics but is most …
Glaisher–Kinkelin constant | Brilliant Math & Science Wiki
Jan 18, 2025 · The Glaisher–Kinkelin constant, usually denoted by the symbol \(A\), is a mathematical constant which is approximately equal to \[ …
Approximating the constants of Glaisher–Kinkelin type
Aug 1, 2013 · It is now known as the Glaisher–Kinkelin constant and its numerical value is given by A ≈ 1.282427130 … . This constant is close connected to the Riemann zeta function ζ, or …
glaisher-kinkelin constant - Wolfram|Alpha
Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history, geography, …
Glaisher constant: Introduction to the classical constants - Wolfram
Glaisher constant The works of H. Kinkelin (1860) and J. Glaisher (1877–1878) introduced one special constant: which was later called the Glaisher or Glaisher‐Kinkelin constant in honor of …
How do you prove this integral involving the Glaisher–Kinkelin …
According to wikipedia on the page Glaisher–Kinkelin constant $$\int_0^{1/2} \ln\Gamma(x) dx=\frac32\ln \text{A}+\frac5{24}\ln 2+\frac14\ln\pi$$ I got interested in how you possibly could …
Glaisher–Kinkelin constant - Taylor & Francis Online
Nov 21, 2011 · The Glaisher–Kinkelin constant is defined by 10 11 16, as well as where G(n) is the Barnes G-function.Barnes 1 defined the double gamma function (or Barnes G-function) …
Glaisher-Kinkelin Constant
May 25, 1999 · where is the Riemann Zeta Function, is Pi, and is the Euler-Mascheroni Constant (Kinkelin 1860, Glaisher 1877, 1878, 1893, 1894). Glaisher (1877) also obtained
Generalized Glaisher-Kinkelin constants and …
Jan 21, 2024 · We study a sequence of constants known as the Bendersky-Adamchik constants which appear quite naturally in number theory and generalize the classical Glaisher-Kinkelin constant. Our main initial purpose is …
Glaisher-Kinkelin Constant Digits -- from Wolfram MathWorld
The decimal expansion of the Glaisher-Kinkelin constant is given by A=1.28242712... (OEIS A074962). A was computed to 5×10^5 decimal digits by E. Weisstein (Dec. 3, 2015).
Automatic sequences and the Glaisher–Kinkelin constant
Jul 1, 2024 · Using a related integration-based approach, and by applying results due to Gosper [22] on integrals involving ln Γ (z + 1), we introduce and prove identities relating automatic …
Glaisher–Kinkelin constant - Wikiwand
In mathematics, the Glaisher–Kinkelin constant or Glaisher's constant, typically denoted A, is a mathematical constant, related to special functions like the K-function and the Barnes G …
Asymptotic expansions related to the Glaisher–Kinkelin constant …
Jun 1, 2016 · In the theory of mathematical constants, the Glaisher–Kinkelin constant or Glaisher's constant, typically denoted by A, is usually defined by the limit (1.1) A = lim n → ∞ n − n 2 / 2 …
Abstract We study a sequence of constants known as the Bendersky-Adamchik constants which appear quite naturally in number theory and generalize the clas-sical Glaisher-Kinkelin …
Convergence of Glaisher-Kinkelin Constant Limit Definitions
Jun 10, 2020 · The Glaisher-Kinkelin constant $A$ is given by the limits $$\begin{align} A&=\lim_{n\rightarrow\infty}\frac{H(n)}{n^{n^2/2+n/2+1/12}e^{-n^2/4}}\\ …
From the Schaar and Lösch-Schoblick integrals to …
2 days ago · In this article, we proposed two integral representations of the logarithm of the Glaisher-Kinkelin constant. Both are based on a definite integral representation involving log …
Asymptotic expansions related to Glaisher–Kinkelin constant …
Aug 1, 2013 · The Glaisher–Kinkelin constant A appears in a number of sums and integrals, especially those involving gamma functions and zeta functions. Finch introduced this constant …
SOME NEW APPROXIMATIONS OF GLAISHER-KINKELIN CONSTANT LI YIN, JU-MEI ZHANG, AND XIU-LI LIN Abstract. In this paper, we established some new approximation …
