Some new continued fraction approximation of Euler's constant

Lu, Dawei; Song, Lixin; Yu, Yang

doi:10.1016/j.jnt.2014.07.002

“…Using continued fractions, Lu et al [23,24] have obtained monotone convergence to γ 0 of the order of O(n −p ), p = 3, 4, 5 (see also Lu [22] and Yang [25]). Kh.…”

Section: )mentioning

confidence: 99%

Acceleration Methods for Series: A Probabilistic Perspective

Adell

¹

,

Lekuona

²

2016

Mediterr. J. Math.

2

0

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Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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“…They proved that, among the sequences , in the case of and the privileged sequence offers the best approximations of γ since Recently, Lu, Song, and Yu [10] provided some approximations of Euler’s constant. A new important sequence was defined as follows: where Two particular sequences were provided as These two sequences converge faster than all other sequences mentioned since for all , …”

Section: Introductionmentioning

confidence: 99%

A series of sequences convergent to Euler’s constant

Jia

¹

,

Ge

²

,

Liu

³

et al. 2018

J Inequal Appl

0

Get access via publisher Add to dashboard Cite

Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

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“…With respect to the first type of computations, we mention that Xu and You [ 2 ] and Lu et al [ 3 , 4 ] have used continued fractions to obtain monotone convergence to γ . For instance, it is shown in [ 2 ], Theorem 2, that where C and are explicit constants, and and are sequences involving the logarithm of a continued fraction, the first one being strictly increasing, and the second one strictly decreasing.…”

Section: Introductionmentioning

confidence: 99%

Monotone and fast computation of Euler’s constant

Adell

¹

,

Lekuona

²

2017

J Inequal Appl

0

Get access via publisher Add to dashboard Cite

Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.

show abstract

Some new continued fraction approximation of Euler's constant

Cited by 17 publications

References 14 publications

Acceleration Methods for Series: A Probabilistic Perspective

Acceleration Methods for Series: A Probabilistic Perspective

A series of sequences convergent to Euler’s constant

Monotone and fast computation of Euler’s constant

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