An Overlooked Series for the Elliptic Perimeter

Linderholm, C. E.; Segal, Arthur C.

doi:10.2307/2691422

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The Binomial Approximation1

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2019

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“…2 not using complex analysis and absolute and uniform convergence of a series, as was used, for example, in [18] 3 considering the identity…”

Section: The Binomial Approximationmentioning

confidence: 99%

The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series

Lampret

2019

Cubo

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For the perimeter P (a, b) of an ellipse with the semi-axes a ≥ b ≥ 0 a sequence Q n (a, b) is constructed such that the relative error of the approximation P (a, b) ≈ Q n (a, b) satisfies the following inequalities 0 ≤ − P (a, b) − Q n (a, b) P (a, b) ≤ (1 − q 2) n+1 (2n + 1) 2 ≤ 1 (2n + 1) 2 e −q 2 (n+1) , true for n ∈ N and q = b a ∈ [0, 1]. RESUMEN Para el perímetro P (a, b) de una elipse con semiejes a ≥ b ≥ 0, se construye una sucesión Q n (a, b) tal que el error relativo de la aproximación P (a, b) ≈ Q n (a, b) satisface las siguientes desigualdades 0 ≤ − P (a, b) − Q n (a, b) P (a, b) ≤ (1 − q 2) n+1 (2n + 1) 2 ≤ 1 (2n + 1) 2 e −q 2 (n+1) , válidas para n ∈ N y q = b a ∈ [0, 1].

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“…2 not using complex analysis and absolute and uniform convergence of a series, as was used, for example, in [18] 3 considering the identity…”

Section: The Binomial Approximationmentioning

confidence: 99%

The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series

Lampret

2019

Cubo

View full text Add to dashboard Cite

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An Overlooked Series for the Elliptic Perimeter

Cited by 1 publication

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The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series

The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series

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An Overlooked Series for the Elliptic Perimeter

Cited by 1 publication

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The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin&#8217;s series

The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin&#8217;s series

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The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series

The perimeter of a flattened ellipse can be estimated accurately even from Maclaurin’s series