Q-Chu-Vandermonde 항등식

이 항목의 수학노트 원문주소

• q-Chu-Vandermonde 항등식

 

 

개요

• 초기하 급수의 합공식 Chu-Vandermonde 공식
  \(\,_2F_1(-n,b;c;1)=\dfrac{(c-b)_{n}}{(c)_{n}}\)
  
• q-analogue 
  

 

\( _2\phi_1(q^{-n},b;c;q,cq^n/b)=\frac{(cq^n;q)_\infty(c/b;q)_\infty}{(c;q)_\infty(cq^n/b;q)_\infty}=\frac{(c/b;q)_n}{(c;q)_n}\)

\(_2\phi_1(q^{-n},b;c;q,q)=\frac{(c/b;q)_n}{(c;q)_n}b^n\)

 

 

 

재미있는 사실

 

• Math Overflow http://mathoverflow.net/search?q=
• 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=
• 수학사연표

 

 

 

 

 

 

수학용어번역

• 단어사전
  
  • http://www.google.com/dictionary?langpair=en%7Cko&q=
  • http://ko.wiktionary.org/wiki/
• 발음사전 http://www.forvo.com/search/
• 대한수학회 수학 학술 용어집
  
  • http://mathnet.kaist.ac.kr/mathnet/math_list.php?mode=list&ftype=eng_term&fstr=
• 남·북한수학용어비교
• 대한수학회 수학용어한글화 게시판

 

 

 

사전 형태의 자료

• http://en.wikipedia.org/wiki/Q-Vandermonde_identity
• http://en.wikipedia.org/wiki/Vandermonde's_identity
• http://mathworld.wolfram.com/q-Chu-VandermondeIdentity.html
• http://en.wikipedia.org/wiki/
• The Online Encyclopaedia of Mathematics
• NIST Digital Library of Mathematical Functions
• The World of Mathematical Equations

 

 

 

 

관련논문

• Some generalized Durfee square identities
  
  • Ira M. Gessel, Discrete MathematicsVolume 49, Issue 1, March 1984, Pages 41-44
    
• Some combinatorial identities associated with the Vandermonde convolution
  
  • H. W. Gould and H. M. Srivastava, 1997
    
• Some Generalizations of Vandermonde's Convolution
  
  • H. W. Gould, The American Mathematical Monthly, Vol. 63, No. 2 (Feb., 1956), pp. 84-91
    

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

 

 

관련도서

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

 

 

링크

• Summaries of Media Coverage of Math
• 구글 블로그 검색
  
  • http://blogsearch.google.com/blogsearch?q=