란덴변환(Landen's transformation)

간단한 소개

 

\(K(\frac{2\sqrt{x}}{1+x})=(1+x)K(x)\)

 

 

 

 

 

관련된 다른 주제들

• 파이값의 계산
• lemniscate 적분

 

표준적인 도서 및 추천도서

• Pi and the AGM
  
  • Jonathan M. Borwein, Peter B. Borwein
• http://www.amazon.com/s/ref=nb_ss_gw?url=search-alias%3Dstripbooks&field-keywords=

 

위키링크

• http://en.wikipedia.org/wiki/Landen%27s_transformation

 

 

참고할만한 자료

• Gauss, Landen, Ramanujan, the Arithmetic-Geometric Mean, Ellipses, π, and the Ladies Diary
  
  • Gert Almkvist and Bruce Berndt
  • The American Mathematical Monthly, Vol. 95, No. 7 (Aug. - Sep., 1988), pp. 585-608