scholarly journals Accurate estimates of (1+x)1/x involved in Carleman inequality and Keller limit

Filomat ◽  
2018 ◽  
Vol 32 (13) ◽  
pp. 4673-4677
Author(s):  
Branko Malesevic ◽  
Yue Hu ◽  
Cristine Mortici
Keyword(s):  
Maclaurin Series ◽  
Carleman Inequality

In this paper, using the Maclaurin series of the functions (1+x)1/x, some inequalities from papers [2] and [5] are generalized. For arbitrary Maclaurin series some general limits of Keller?s type are defined and applying for generalization of some well known results.

scholarly journals On The Tails of the Exponential Series

1994 ◽  
Vol 37 (2) ◽  
pp. 278-286 ◽  
Author(s):  
C. Yalçin Yildirim
Keyword(s):  
Zeta Function ◽  
Riemann Zeta Function ◽  
Partial Sums ◽  
Maclaurin Series ◽  
Exponential Series ◽  
Asymptotic Estimation ◽  
The Riemann Zeta Function ◽  
Riemann Zeta

AbstractA relation between the zeros of the partial sums and the zeros of the corresponding tails of the Maclaurin series for ez is established. This allows an asymptotic estimation of a quantity which came up in the theory of the Riemann zeta-function. Some new properties of the tails of ez are also provided.

scholarly journals Correction factor determination on failure rate equation of MacLaurin series for low and high mode application

2016 ◽  
Vol 7 (2) ◽  
pp. 827-834
Author(s):  
Totok R. Biyanto ◽  
Franky Kusuma ◽  
Ali Musyafa ◽  
Ronny Dwi Noriyati ◽  
Ridho Bayuaji ◽  
...  
Keyword(s):  
Failure Rate ◽  
Correction Factor ◽  
Rate Equation ◽  
High Mode ◽  
Maclaurin Series

scholarly journals Relationship and discrepancies between the Extended-Rydberg and the Generalized Buckingham potential energy functions

2007 ◽  
Vol 72 (2) ◽  
pp. 159-164 ◽  
Author(s):  
Teik-Cheng Lim
Keyword(s):  
Molecular Modeling ◽  
Lower Energy ◽  
Interatomic Distance ◽  
Energy Difference ◽  
Maclaurin Series ◽  
Energy Functions ◽  
Finite Distortion ◽  
Potential Energy Functions ◽  
Buckingham Potential ◽  
Interatomic Energy

This paper relates the interatomic energy according to the Extended-Rydberg and the Generalized Buckingham potential functions by applying a Maclaurin series expansion on the latter and thereafter comparing it with the former. In so doing, the plotted curves of these two functions not only show equal curvature at the equilibrium state, but also reveal a discrepancy for the finite distortion. It is shown that, when equated at equilibrium, the Generalized Buckingham gives a lower energy in comparison to the Extended-Rydberg at finite bond compression and stretching. However, the energy difference diminishes when the interatomic distance exceeds twice that at equilibrium. Due to such discrepancies upon comparative normalization, it would be beneficial for computational chemists to select the appropriate potential function for the purpose of conservative molecular modeling. .

Karamata Renewed and Local Limit Results

2006 ◽  
Vol 58 (5) ◽  
pp. 1026-1094
Author(s):  
David Handelman
Keyword(s):  
Positive Constant ◽  
Additional Condition ◽  
Local Limit ◽  
Unit Interval ◽  
Open Unit ◽  
Precise Asymptotics ◽  
Maclaurin Series ◽  
Real Analytic Functions ◽  
Real Analytic ◽  
A Minor

AbstractConnections between behaviour of real analytic functions (with no negative Maclaurin series coefficients and radius of convergence one) on the open unit interval, and to a lesser extent on arcs of the unit circle, are explored, beginning with Karamata's approach. We develop conditions under which the asymptotics of the coefficients are related to the values of the function near 1; specifically, a(n) ∼ f(1 – 1/n)/αn (for some positive constant α), where f(t) = Σa(n)tn. In particular, if F = Σc(n)tn where c(n) ≥ 0 and Σc(n) = 1, then f defined as (1 – F)–1 (the renewal or Green's function for F) satisfies this condition if F′ does (and a minor additional condition is satisfied). In come cases, we can show that the absolute sum of the differences of consecutiveMaclaurin coefficients converges. We also investigate situations in which less precise asymptotics are available.

Behavior of Coefficients of Inverses of α-Spiral Functions

1986 ◽  
Vol 38 (6) ◽  
pp. 1329-1337 ◽  
Author(s):  
Richard J. Libera ◽  
Eligiusz J. Złotkiewicz
Keyword(s):  
Unit Disk ◽  
Series Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Maclaurin Series ◽  
Koebe Function ◽  
One To One ◽  
Image Position

If f(z) is univalent (regular and one-to-one) in the open unit disk Δ, Δ = {z ∊ C:│z│ < 1}, and has a Maclaurin series expansion of the form(1.1)then, as de Branges has shown, │ak│ = k, for k = 2, 3, … and the Koebe function.(1.1)serves to show that these bounds are the best ones possible (see [3]). The functions defined above are generally said to constitute the class .

scholarly journals p-Trigonometric andp-Hyperbolic Functions in Complex Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-18
Author(s):  
Petr Girg ◽  
Lukáš Kotrla
Keyword(s):  
Differential Equations ◽  
Complex Domain ◽  
Trigonometric Functions ◽  
Maclaurin Series ◽  
Hyperbolic Functions

We study extension ofp-trigonometric functionssinpandcospand ofp-hyperbolic functionssinhpandcoshpto complex domain. Our aim is to answer the question under what conditions onpthese functions satisfy well-known relations for usual trigonometric and hyperbolic functions, such as, for example,sin(z)=-i·sinh⁡i·z. In particular, we prove in the paper that forp=6,10,14,…thep-trigonometric andp-hyperbolic functions satisfy very analogous relations as their classical counterparts. Our methods are based on the theory of differential equations in the complex domain using the Maclaurin series forp-trigonometric andp-hyperbolic functions.

Toward Identifying Consumer Responsibility on Voltage Distortion and Filtering Based on the Maclaurin Series

2020 ◽  
Vol 67 (12) ◽  
pp. 3467-3471
Author(s):  
Cesar David Paredes Crovato ◽  
Rodrigo Ivan Goytia Mejia ◽  
Rodrigo da Rosa Righi
Keyword(s):  
Maclaurin Series ◽  
Voltage Distortion ◽  
Consumer Responsibility
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