Last edited by Goshakar
Thursday, October 22, 2020 | History

2 edition of generalized Euler-Mascheroni constants found in the catalog.

generalized Euler-Mascheroni constants

O. R. Ainsworth

# generalized Euler-Mascheroni constants

## by O. R. Ainsworth

Subjects:
• Euler"s numbers.,
• Functions, Zeta.,
• Mathematical analysis.,
• Laurent series.

• Edition Notes

The Physical Object ID Numbers Statement O.R. Ainsworth and L.W. Howell. Series NASA technical paper -- 2264. Contributions Howell, Leonard W., United States. National Aeronautics and Space Administration. Scientific and Technical Information Office., George C. Marshall Space Flight Center. Pagination 12 p. ; Number of Pages 12 Open Library OL15306034M

FAST CONVERGENCES TOWARDS EULER-MASCHERONI CONSTANT More precisely, we mention the following results related to the speed of con-vergence of the sequence (γ n) ≥1: 1 2(n +1). Dec 07,  · The Euler-Mascheroni constant $\gamma$ comes up when evaluating the harmonic numbers. It turns out, however, that $\gamma$ also appears in other (unexpected) cases, see below. The $n$'th harmonic number [math]H_n[/.

No quadratically converging algorithm for computing is known (Bailey ). 7,, digits of have been computed as of Feb. (Plouffe). See also Euler Product, Mertens Theorem, Stieltjes Constants. References. Bailey, D. H. Numerical Results on the Transcendence of Constants Involving,, and Euler's Constant.'' Math. Mar 17,  · Among the many constants that appear in mathematics, π, e, and i are the most familiar. Following closely behind is y, or gamma, a constant that arises in many mathematical areas yet maintains a profound sense of mystery. In a tantalizing blend of history and mathematics, Julian Havil takes the reader on a journey through logarithms and the harmonic series, the two,/5.

Nov 01,  · Read "A solution to an open problem on the Euler–Mascheroni constant, Applied Mathematics and Computation" on DeepDyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. THE EULER-MASCHERONI CONSTANT AND THE HARM ONIC SERIES During our discussion on Bessel functions of the second kind we encountered the Euler-Mascheroni constant defined as-This important constant represents the difference between the harmonic series which is known to be divergent and the logarithm of infinity.

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### Generalized Euler-Mascheroni constants by O. R. Ainsworth Download PDF EPUB FB2

THE GENERALIZED EULER-MASCHERONI CONSTANTS By 0. Ainsworth and L. Howell The information in this report has been reviewed for technical content.

Review of any information concerning Department of Defense or nuclear energy activities or programs has been made by the MSFC Security Classification Officer. Note: Citations are based on reference standards. However, formatting rules can vary widely between applications and fields of interest or study.

The specific requirements or preferences of your reviewing publisher, classroom teacher, institution or organization should be applied. The Euler–Mascheroni constant (also called Euler's constant) is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma (γ).

It is defined as the limiting difference between the harmonic series and the natural logarithm. arXivv1 [hamaikastudio.com] 23 Dec Sharp Estimates of the Generalized Euler-Mascheroni Constant Ti-Ren Huang1∗, Bo-Wen Han 1, You-Ling Liu2, Xiao-Yan Ma1 1 Department of Mathematics, Zhejiang Sci-Tech University, HangzhouChina.

A large number of series and integral representations for the Stieltjes constants (or generalized Euler-Mascheroni constants) {\gamma}_k and the generalized Stieltjes constants {\gamma}_k(a) have.

May 18,  · In the article, we provide several sharp upper and lower bounds for the generalized Euler–Mascheroni constant $$\gamma (a)$$. As applications, we improve some previously results on the Euler–Mascheroni constant γ. The idea presented may stimulate further research in Cited by: We propose new simple sequences approximating the Euler–Mascheroni constant and its generalization, which converge faster towards their limits than those considered by DeTemple [D.W.

DeTemple, A quicker convergence to Euler’s constant, Am. Math. Monthly (5) () –], Sîntămărian [A. Sîntămărian, A generalization of Euler’s constant, hamaikastudio.com by: Generalized Euler constants and the Riemann hypothesis 46 The constant γ is often known as the Euler-Mascheroni constant, after later work the popular book of J.

Havil [] devoted extensively to mathematics around Euler’s constant, and Finch [, Sections and ].Cited by: Stack Exchange network consists of Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share.

Get this from a library. An integral representation of the generalized Euler-Mascheroni constants. [O R Ainsworth; Leonard W Howell; United States. National Aeronautics and Space Administration.

Scientific and Technical Information Branch.]. Transcendence of Generalized Euler Constants Author(s): M. Ram Murty, Anastasia Zaytseva suggest [4], which is a new book by Havil devoted to the Euler constant.

There are several generalizations of. InLehmer [5] introduced the class of analogues of the Euler constant described below. A GENERALIZATION OF EULER™S CONSTANT MARK HEDLEY 1. History of and the intent to study P n k=0 1 k+1. The EulerŒMascheroni constant, sometimes shortened to Author: Mark Hedley.

Then the generalized Euler-Mascheroni constant γ (a) [1] is given by γ (a) = lim Recently, the two bounds for γ and γ (a) have attracted the attention of many mathe- maticians. The Euler-Mascheroni constant, also known as Euler's constant or simply "gamma," is a constant that appears in many problems in analytic number theory and calculus.

It is denoted by γ, \gamma, γ, and the first few digits of this constant are as follows. Numbers, constants and computation 1 It is also known as the Euler-Mascheroni constant. According to Glaisher [4], the use of the symbol γ is probably due to the geometer Lorenzo Mascheroni () who used it in while Euler used the letter C.

The constant γ is deeply related to the Gamma function Γ(x) thanks to the. AN INTEGRAL REPRESENTATION OF THE GENERALIZED EU LER-MASCHERON I CONSTANTS The generalized Euler-Mascheroni constants are defined by and are coefficients of the Laurent expansion of the Riemann Zeta function {(z) about z = 1 1 O0 (-1)n yn (z-1)" S(Z) = - + c, Re(z) Z 0.

z- 1 n. n=O. Stieltjes Constants Generalized Gamma Functions Liouville–Roth Constants Diophantine Approximation Constants Self-Numbers Density Constant Cameron’s Sum-Free Set Constants Triple-Free Set Constants Erdos¨ –Lebensold Constant Finite Case Inﬁnite.

The Euler–Mascheroni constant γ = is defined in mathematics as the limit of the sequence γ n = 1 + 1 2 + 1 3 + ⋯ + 1 n − ln n and it has numerous applications in many areas of pure and applied mathematics, such as analysis, theory of probability, special functions, applied statistics, or Cited by: The Euler–Mascheroni constant is a mathematical constant recurring in analysis and number theory, usually denoted by the lowercase Greek letter gamma.

"Expansions of generalized Euler's constants into the series of polynomials in Second edition of the book Binary numberBinary: EULER-MASCHERONI CONSTANT In studying the difference between the divergent area under the curve F(x)=1/x from x=1 to infinity and the area under the staircase function where we have– 1 1 () in n x n n S x, the Swiss mathematician Leonard Euler found back in that the area equals the constant value γ=.

Mascheroni has written only one paper about Euler's Constant (). He use only hamaikastudio.coming de:David Bierens de Haan using A, Glaisher should be corrected with "De Haan and Mascheroni A; De Morgan, Boole, &c., have written it γ".There are a lot of early papers about the hamaikastudio.com there was a famous discussion about the constant of the Logarithmic integral function (which (Rated B-class, Mid-importance): WikiProject Mathematics.Series representations (18 formulas) EulerGamma.

Constants EulerGamma.hamaikastudio.comlofInequalitiesandApplications Page3of9 α 4 (a+n–1)6≤γ(a)–μ n(a)0andn≥n 0 Cited by: