부정적분의 초등함수 표현(Integration in finite terms)

 

 

 

 

 

 

관련된 다른 주제들

• 타원적분, 타원함수, 타원곡선
• 일반적인 5차 이상의 방정식의 대수적 해가 존재하지 않음에 대한 아벨의 증명

 

표준적인 도서 및 추천도서

• Integration in finite terms: Liouville's theory of elementary methods
  
  • Joseph Fels Ritt

 

위키링크

• http://en.wikipedia.org/wiki/Differential_Galois_theory

 

 

참고할만한 자료

• The Problem of Integration in Finite Terms
  
  • Robert H. Risch, Transactions of the American Mathematical Society, Vol. 139, (May, 1969), pp. 167-189
• Integration in Finite Terms
  
  • Maxwell Rosenlicht, The American Mathematical Monthly, Vol. 79, No. 9 (Nov., 1972), pp. 963-972

• Integration in Finite Terms: The Liouville Theory
  
  • Toni Kasper, Mathematics Magazine, Vol. 53, No. 4 (Sep., 1980), pp. 195-201
• An Invitation to Integration in Finite Terms
  
  • Elena Anne Marchisotto and Gholam-Ali Zakeri, The College Mathematics Journal, Vol. 25, No. 4 (Sep., 1994), pp. 295-308
• From analytic to algebraic methods. Liouville’s approach to integration in finite terms
  
  • Jesper Lützen, NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin, Volume 2, Number 1 / 1994년 12월
• Integration in elementary terms
  
  • Brian Conrad
• On solvability and unsolvability of equations in explicit form
  
  • A G Khovanskii, Russian Math. Surveys 2004, 59 (4), 661-736