이항급수와 이항정리

 

 

개요

\((1 + x)^\alpha = \sum_{k=0}^{\infty} {\alpha \choose k} x^k = 1 + \alpha x + \frac{\alpha(\alpha-1)}{2!} x^2 + \frac{\alpha(\alpha-1)(\alpha-2)}{3!} x^3 +\cdots\)

\(\frac{1}{(1-z)^a}=\sum_{n=0}^{\infty}\frac{(a)_n}{n!}z^n=1+az+\frac{a(a+1)}{2!}z^2+\frac{a(a+1)(a+2)}{3!}z^3+\cdots = \,_1F_0(a;z)\)

 

• Pochhammer 기호와 캐츠(Kac) 기호
  

 

 

예

\(\frac{1}{\sqrt{1-4z}}=\sum_{n=0}^{\infty} {{2n}\choose {n}} z^n\)

 

 

재미있는 사실

 

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

 

 

역사

• http://www.google.com/search?hl=en&tbs=tl:1&q=newton+binomial
• 수학사연표

 

 

 

 

 

 

수학용어번역

• http://www.google.com/dictionary?langpair=en%7Cko&q=
• 대한수학회 수학 학술 용어집
  
  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
• 대한수학회 수학용어한글화 게시판

 

 

사전 형태의 자료

• http://ko.wikipedia.org/wiki/
• [1]http://en.wikipedia.org/wiki/binomial_theorem
• http://en.wikipedia.org/wiki/Binomial_series
• http://www.wolframalpha.com/input/?i=
• NIST Digital Library of Mathematical Functions
• The On-Line Encyclopedia of Integer Sequences
  
  • http://www.research.att.com/~njas/sequences/?q=

 

 

관련논문

• http://www.jstor.org/action/doBasicSearch?Query=
• http://dx.doi.org/

 

관련도서 및 추천도서

• 도서내검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/contentSearch.do?query=
• 도서검색
  
  • http://books.google.com/books?q=
  • http://book.daum.net/search/mainSearch.do?query=
  • http://book.daum.net/search/mainSearch.do?query=

 

 

관련기사

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

 

 

블로그

• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=
• 네이버 오늘의과학
• 수학동아
• Mathematical Moments from the AMS
• BetterExplained