푸크스 미분방정식(Fuchsian differential equation)

이 항목의 스프링노트 원문주소

• Fuchsian 미분방정식(Fuchsian differential equation)
  

 

 

개요

• 선형미분방정식
  \(\frac{d^n w}{dz^n} + A_1(z)\frac{d^{n-1}w}{dz^{n-1}} + \cdots + A_{n-1}(z)\frac{dw}{dz} + A_n(z)w=0\)
  모든 특이점이 정규특이점(regular singular points)인 경우, 이를 Fuchsian 미분방정식이라 한다
  
• 19세기에 많은 연구가 진행되었음
  

• 초기하 미분방정식(Hypergeometric differential equations) 은 대표적인 Fuchsian 미분방정식의 예이다
  

 

 

역사

 

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

 

 

메모

• Group Theory and Differential Equations
  University of Minnesota Lecture Notes 1959-1960
  by Lawrence Markus   (with permission of the author)
  
• http://www.ima.umn.edu/~miller/Group_Theory_and_Differential_Equations.html
  

 

 

관련된 항목들

• 슈워츠 목록
  

 

 

수학용어번역

• 단어사전 http://www.google.com/dictionary?langpair=en%7Cko&q=
• 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://ko.wikipedia.org/wiki/
• http://en.wikipedia.org/wiki/
• http://www.proofwiki.org/wiki/
• 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

• Liouvillian First Integrals of Differential Equations
  
  • Michael F. Singer, Transactions of the American Mathematical Society, Vol. 333, No. 2 (Oct., 1992), pp. 673-688
• Algebraic Relations Among Solutions of Linear Differential Equations: Fano's Theorem
  
  • Michael F. Singer, American Journal of Mathematics, Vol. 110, No. 1 (Feb., 1988), pp. 115-143
• Elementary and Liouvillian solutions of linear differential equations
  
  • M. F. Singer and J. H. Davenport, 1985
• Some Applications of Linear Groups to Differential Equations
  
  • Michael F. Singer and Marvin D. Tretkoff, American Journal of Mathematics, Vol. 107, No. 5 (Oct., 1985), pp. 1111-1121
• Logarithmic singularities of Fuchs equations, and a criterion for the monodromy group to be finite
  
  • N. V. Grigorenko, MATHEMATICAL NOTESVolume 33, Number 6, 453-454
• Liouvillian Solutions of n-th Order Homogeneous Linear Differential Equations
  
  • Michael F. SingerAmerican Journal of Mathematics, Vol. 103, No. 4 (Aug., 1981), pp. 661-682
• Algebraic Solutions of nth Order Linear Differential Equations
  
  • M. Singer, Proceedings of the Queen's University 1979 Conference on Number Theory, Queens Papers in Pure and Applied Mathematics, (54), pp. 379-420
• On Second Order Linear Differential Equations with Algebraic Solutions
  
  • F. Baldassari, B. Dwork, American Journal of Mathematics, Vol. 101, No. 1 (Feb., 1979), pp. 42-76
• http://www.jstor.org/action/doBasicSearch?Query=fuchsian+differential
• http://www.ams.org/mathscinet
• http://dx.doi.org/10.1007/3-540-15984-3_335

 

 

관련도서

• Linear Differential Equations and Group Theory from Riemann to Poincare
  
  • Jeremy J. Gray,  2008(2판)
• Lectures on algebraic solutions of hypergeometric differential equations
  
  • Matsuda, Michihiko, 1985
• 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=