차분방정식(difference equation) 과 유한미적분학 (finite calculus)

간단한 소개

• 수열의 합을 다루는 데 유용한 테크닉
• 미적분학의 개념과 대응되는 점이 있음.
  
  • 계차수열 ~ 미분
  • 부분합 ~ 적분

 

 

 

 

 

관련된 다른 주제들

• Sum of powers
• 생성함수

 

 

 

 

 

참고할만한 자료

• The Finite Calculus
  
  • From the book 'A Primer of Analytic Number Theory' 1.2
• Using the Finite Difference Calculus to Sum Powers of Integers
  
  • Lee Zia
  • The College Mathematics Journal, Vol. 22, No. 4 (Sep., 1991), pp. 294-300

• Sums and Differences vs. Integrals and Derivatives
  
  • Gilbert Strang
  • The College Mathematics Journal, Vol. 21, No. 1 (Jan., 1990), pp. 20-27

• An Elementary Exposition of the Theory of Finite Differences
  
  • Saul Epsteen
  • The American Mathematical Monthly, Vol. 11, No. 6/7 (Jun. - Jul., 1904), pp. 131-136
• Telescoping Sums and the Summation of Sequences
  
  • G. Baley Price
  • The Two-Year College Mathematics Journal, Vol. 4, No. 2 (Spring, 1973), pp. 16-29
• 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