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New properties of the lemniscate function and its transformation.

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Title: New properties of the lemniscate function and its transformation.
Authors: Nishimura, Ryo1 rrnishimura@gmail.com
Source: Journal of Mathematical Analysis & Applications. Jul2015, Vol. 427 Issue 1, p460-468. 9p.
Subjects: Lemniscates, Mathematical functions, Mathematical transformations, Infinity (Mathematics), Algorithms, Geometric analysis
Abstract: In this paper, we show several formulas for the lemniscate function which include an infinite product formula for the lemniscate sine. Furthermore, we show the relation between the product formula and Carlson's algorithm which is known as the variant of the arithmetic geometric mean of Gauss. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 101499561
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: New properties of the lemniscate function and its transformation.
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  Data: <searchLink fieldCode="AR" term="%22Nishimura%2C+Ryo%22">Nishimura, Ryo</searchLink><relatesTo>1</relatesTo><i> rrnishimura@gmail.com</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Mathematical+Analysis+%26+Applications%22">Journal of Mathematical Analysis & Applications</searchLink>. Jul2015, Vol. 427 Issue 1, p460-468. 9p.
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  Data: <searchLink fieldCode="DE" term="%22Lemniscates%22">Lemniscates</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+transformations%22">Mathematical transformations</searchLink><br /><searchLink fieldCode="DE" term="%22Infinity+%28Mathematics%29%22">Infinity (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+analysis%22">Geometric analysis</searchLink>
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  Label: Abstract
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  Data: In this paper, we show several formulas for the lemniscate function which include an infinite product formula for the lemniscate sine. Furthermore, we show the relation between the product formula and Carlson's algorithm which is known as the variant of the arithmetic geometric mean of Gauss. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Journal of Mathematical Analysis & Applications is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.jmaa.2015.02.066
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      – Code: eng
        Text: English
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      – SubjectFull: Lemniscates
        Type: general
      – SubjectFull: Mathematical functions
        Type: general
      – SubjectFull: Mathematical transformations
        Type: general
      – SubjectFull: Infinity (Mathematics)
        Type: general
      – SubjectFull: Algorithms
        Type: general
      – SubjectFull: Geometric analysis
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      – TitleFull: New properties of the lemniscate function and its transformation.
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              Text: Jul2015
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              Y: 2015
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