Glaisher constant

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August undefined, 2024

WebGlaisher == 2^(9/32) E^(29/192 + EulerGamma/96 + (3 Zeta[3])/(64 Pi^2) + Derivative[1][Zeta][-1] - 2 Derivative[1, 0][Zeta][-2, 1/4]) Pi^(1/32) (Product[(4 k + 1)^(1 ... WebFeb 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 …

Some Approximations of Glaisher–Kinkelin and Bendersky

WebIn this paper, we provide some new logarithm and polynomial approximations, inequalities and rates of convergence of Glaisher–Kinkelin’s and Bendersky–Adamchik’s constants. To demonstrate ... WebAug 1, 2013 · The results. Regarding the problem of approximation of the Glaisher–Kinkelin constant, we give the following. Theorem 1. For every n ⩾ 1, we have w n − 1 720 n 2 + 1 5040 n 4 − 1 10 080 n 6 < ln A < w n − 1 720 n 2 + 1 5040 n 4, where w n = ∑ k = 1 n k ln k − ( n 2 2 + n 2 + 1 12) ln n + n 2 4. pk movie villain

Approximating the constants of Glaisher–Kinkelin type

WebGlaisher Notations Traditional name Glaisher constant Traditional notation A Mathematica StandardForm notation Glaisher Primary definition 02.08.02.0001.01 A−exp 1 12-z¢H … WebCatalan (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 Extreme value distribution ... WebGlaisher is the symbol representing Glaisher's constant , also known as the Glaisher – Kinkelin constant. Glaisher has a number of equivalent definitions throughout … pkk taksim

(PDF) Some New Convergent Sequences of Glaisher–Kinkelin’s …

Glaisher - Wolfram

WebEuler's constant (sometimes called the Euler–Mascheroni constant) is a mathematical constant, usually denoted by the lowercase Greek letter gamma (γ), defined as the limiting difference between the harmonic series and the natural logarithm, denoted here by log: = (⁡ + =) = (+ ⌊ ⌋). Here, ⌊ ⌋ represents the floor function. The numerical value of Euler's … WebGlaisher-Kinkelin Constant Continued Fraction. Download Wolfram Notebook. The continued fraction of is [1; 3, 1, 1, 5, 1, 1, 1, 3, 12, 4, 1, 271, 1, ...] (OEIS A087501 ). A plot of the first 256 terms of the continued fraction represented as a sequence of binary bits is … pkna onlineWebGlaisher 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 commonly defined as the constant that satisfies , where is the Riemann zeta function Zeta, is its derivative evaluated at , and Log is the natural logarithm. Glaisher … hallo ikea kissen

"WebThis article uses bare URLs, which are uninformative and vulnerable to link rot. Please consider converting them to full citations to ensure the article remains verifiable and maintains a consistent citation style. Several templates and tools are available to assist in formatting, such as Reflinks (documentation), reFill (documentation) and Citation bot … " - Glaisher constant

Glaisher constant

Approximating the constants of Glaisher–Kinkelin type

WebGlaisher 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 its founders. This constant is used in number theory, Bose‐Einstein and Fermi‐Dirac statistics, analytic approximation and evaluation of integrals ... WebJames Whitbread Lee Glaisher. James Whitbread Lee Glaisher FRS FRSE FRAS (5 November 1848, Lewisham [1] – 7 December 1928, Cambridge ), son of James Glaisher and Cecilia Glaisher, was a prolific English mathematician and astronomer. [2] [3] His large collection of (mostly) English ceramics was mostly left to the Fitzwilliam Museum in …

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WebNov 21, 2011 · Abstract. (i) The Glaisher–Kinkelin constant A=1.28242712… is defined as the limit of the sequence . We establish the asymptotic representation of the sequence … In mathematics, the Glaisher–Kinkelin constant or Glaisher's constant, typically denoted A, is a mathematical constant, related to the K-function and the Barnes G-function. The constant appears in a number of sums and integrals, especially those involving gamma functions and zeta functions. It is named after mathematicians James Whitbread Lee Glaisher and Hermann Kinkelin. Its approximate value is:

WebFeb 21, 2024 · Abstract. In this paper, we provide some new sequences to approximate the Glaisher–Kinkelin constant and Bendersky–Adamchik constant, which are faster than the approximations in literature (Dawei and Mortici in J Number Theory 144:340–352, 2014; Mortici in J Number Theory 133:2465–2469, 2013 ). Download to read the full article text. WebThe 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). The Earls sequence (starting position of n copies of the digit n) for e is given for n=1, 2, ... by 7, 14, 2264, 1179, 411556, ... (OEIS A225763). The digit sequences 0123456789 and …

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.

WebAug 1, 2013 · Chen [15] established the asymptotic expansions related to the Glaisher-Kinkelin constant A and the Choi-Srivastava constants B and C. Mortici [54] also dealt with the same problem. Cheng and Chen ...

• Glaisher's theorem • Glaisher–Kinkelin constant hallo hyperWebDefinitions of classical constants and the imaginary unit. 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 logarithm) , Euler-Mascheroni constant (Euler gamma) , Catalan number (Catalan's constant) , Glaisher constant … hallo huisWebNov 15, 2024 · In this paper we provide some relationships between Catalan’s constant and the 3 F 2 and 4 F 3 hypergeometric functions, deriving them from some parametric integrals. In particular, using the complete elliptic integral of the first kind, we found an alternative proof of a result of Ramanujan for 3 F 2, a second identity related to 4 F 3 and ... pk mittehttp://www.wukong2024.com/v_88023.html pkmr manhattan kshttp://numbers.computation.free.fr/Constants/Gamma/gamma.pdf hallo huhuWebSep 1, 2024 · Glaisher–Kinkelin constant, Bendersky–Adamc hik constant, rate of convergence, multiple-correction. 1. Introduction. In the theory of mathematical constants, it is very important to construct. pk muotilinjaWebGlaisher : Introduction to the classical constants: Constants: Glaisher (31 formulas) Primary definition (1 formula) Specific values (1 formula) General characteristics (0 formulas) Series representations (1 formula) Integral representations (1 formula) Product representations (3 … halloids