Asymptotic expansion and bounds for complete elliptic integrals

Miao Kun Wang; Yu Ming Chu; Yong Min Li; Wen Zhang

doi:10.7153/mia-2020-23-67

Asymptotic expansion and bounds for complete elliptic integrals

Miao Kun Wang, Yu Ming Chu, Yong Min Li, Wen Zhang

Research output: Contribution to journal › Article › peer-review

35 Scopus citations

Abstract

In the article, we present several new bounds for the the complete elliptic integrals K (r) = | ₀^π /²(1−r² sin² θ )⁻1/²dθ and E (r) = | ₀^π /² (1−r² sin² θ )¹/²dθ , and find an asymptotic expansion for K (r) as r → 1, which are the refinements and improvements of the previously well-known results.

Original language	English
Pages (from-to)	821-841
Number of pages	21
Journal	Mathematical Inequalities and Applications
Volume	23
Issue number	3
DOIs	https://doi.org/10.7153/mia-2020-23-67
State	Published - 2020

Keywords

Arithmetic-geometric mean
Asymptotic expansion
Bound
Complete elliptic integrals
Infinite series

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title = "Asymptotic expansion and bounds for complete elliptic integrals",

abstract = "In the article, we present several new bounds for the the complete elliptic integrals K (r) = | 0π /2(1−r2 sin2 θ )−1/2dθ and E (r) = | 0π /2 (1−r2 sin2 θ )1/2dθ , and find an asymptotic expansion for K (r) as r → 1, which are the refinements and improvements of the previously well-known results.",

keywords = "Arithmetic-geometric mean, Asymptotic expansion, Bound, Complete elliptic integrals, Infinite series",

author = "Wang, {Miao Kun} and Chu, {Yu Ming} and Li, {Yong Min} and Wen Zhang",

year = "2020",

doi = "10.7153/mia-2020-23-67",

language = "English",

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pages = "821--841",

journal = "Mathematical Inequalities and Applications",

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T1 - Asymptotic expansion and bounds for complete elliptic integrals

AU - Wang, Miao Kun

AU - Chu, Yu Ming

AU - Li, Yong Min

AU - Zhang, Wen

PY - 2020

Y1 - 2020

N2 - In the article, we present several new bounds for the the complete elliptic integrals K (r) = | 0π /2(1−r2 sin2 θ )−1/2dθ and E (r) = | 0π /2 (1−r2 sin2 θ )1/2dθ , and find an asymptotic expansion for K (r) as r → 1, which are the refinements and improvements of the previously well-known results.

AB - In the article, we present several new bounds for the the complete elliptic integrals K (r) = | 0π /2(1−r2 sin2 θ )−1/2dθ and E (r) = | 0π /2 (1−r2 sin2 θ )1/2dθ , and find an asymptotic expansion for K (r) as r → 1, which are the refinements and improvements of the previously well-known results.

KW - Arithmetic-geometric mean

KW - Asymptotic expansion

KW - Bound

KW - Complete elliptic integrals

KW - Infinite series

UR - http://www.scopus.com/inward/record.url?scp=85089855302&partnerID=8YFLogxK

U2 - 10.7153/mia-2020-23-67

DO - 10.7153/mia-2020-23-67

M3 - Article

AN - SCOPUS:85089855302

SN - 1331-4343

VL - 23

SP - 821

EP - 841

JO - Mathematical Inequalities and Applications

JF - Mathematical Inequalities and Applications

IS - 3

ER -

Asymptotic expansion and bounds for complete elliptic integrals

Abstract

Keywords

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