A new form of the generalized complete elliptic integrals

研究成果: Article査読

26 被引用数 (Scopus)

抄録

Generalized trigonometric functions are applied to Legendre’s form of complete elliptic integrals, and a new form of the generalized complete elliptic integrals of the Borweins is presented. According to the form, it can be easily shown that these integrals have similar properties to the classical ones. In particular, it is possible to establish a computation formula of the generalized p in terms of the arithmeticgeometric mean, in the classical way as the Gauss-Legendre algorithm for p by Brent and Salamin. Moreover, an elementary alternative proof of Ramanujan’s cubic transformation is also given.

本文言語English
ページ(範囲)202-226
ページ数25
ジャーナルKodai Mathematical Journal
39
1
DOI
出版ステータスPublished - 2016 3 25

ASJC Scopus subject areas

  • Mathematics(all)

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