오일러-맥클로린 공식

간단한 소개

• 수열의 합과 적분을 연결해주는 공식

 

\(\sum_{i=0}^n f(i) = \int^n_0f(x)\,dx-B_1(f(n)+f(0))+\sum_{k=2}^p\frac{B_k}{k!}\left(f^{(k-1)}(n)-f^{(k-1)}(0)\right)+R\)

\(\left|R\right|\leq\frac{2}{(2\pi)^{2(p+1)}}\int_0^n\left|f^{(p)}(x)\right|\,dx\)

\(B_0=1\), \(B_1=-{1 \over 2}\), \(B_2={1\over 6}\), \(B_3=0\), \(B_4=-\frac{1}{30}\), \(B_5=0\), \(B_6=\frac{1}{42}\)

 

 

응용

• 스털링 공식
• 거듭제곱의 합을 구하는 공식

 

 

 

 

 

 

 

 

많이 나오는 질문

• 네이버 지식인
  
  • http://kin.search.naver.com/search.naver?where=kin_qna&query=

 

관련된 고교수학 또는 대학수학

• 일변수미적분학

 

관련된 다른 주제들

• 스털링 공식
• 거듭제곱의 합을 구하는 공식

 

관련도서 및 추천도서

• 도서내검색
  
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• 도서검색
  
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  • http://book.daum.net/search/mainSearch.do?query=

 

참고할만한 자료

• Euler-Maclaurin summation formula (pdf)
  
  • E. Hairer (Author), G. Wanner
  • From Analysis by Its History, 160-169p
• Dances between continuous and discrete: Euler's summation formula
  
  • David J. Pengelley
  • in: Robert Bradley and Ed Sandifer (Eds), Proceedings, Euler 2K+2 Conference (Rumford, Maine, 2002) , Euler Society, 2003.
• An Elementary View of Euler's Summation Formula
  
  • Tom M. Apostol
  • The American Mathematical Monthly, Vol. 106, No. 5 (May, 1999), pp. 409-418
• The Euler-Maclaurin and Taylor Formulas: Twin, Elementary Derivations
  
  • Vito Lampret
  • Mathematics Magazine, Vol. 74, No. 2 (Apr., 2001), pp. 109-122
• An Euler Summation Formula
  
  • Irwin Roman
  • The American Mathematical Monthly, Vol. 43, No. 1 (Jan., 1936), pp. 9-21
• http://ko.wikipedia.org/wiki/오일러
• http://en.wikipedia.org/wiki/Euler's_summation_formula
• http://viswiki.com/en/
• http://front.math.ucdavis.edu/search?a=&t=&c=&n=40&s=Listings&q=
• http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=ALLF&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All&s7=
• 다음백과사전 http://enc.daum.net/dic100/search.do?q=
• 대한수학회 수학 학술 용어집

 

관련기사

• 네이버 뉴스 검색 (키워드 수정)
  
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  • http://news.search.naver.com/search.naver?where=news&x=0&y=0&sm=tab_hty&query=

 

 

블로그

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이미지 검색

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• http://images.google.com/images?q=
• http://www.artchive.com

 

동영상

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