"홀로노믹 수열"의 두 판 사이의 차이
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==관련논문== | ==관련논문== | ||
| + | * Ekhad, Shalosh B., and Doron Zeilberger. “The C-Finite Ansatz Meets the Holonomic Ansatz.” arXiv:1512.06902 [math], December 21, 2015. http://arxiv.org/abs/1512.06902. | ||
* Wimp, Jet, and Doron Zeilberger. 1985. “Resurrecting the Asymptotics of Linear Recurrences.” Journal of Mathematical Analysis and Applications 111 (1) (October): 162–176. doi:10.1016/0022-247X(85)90209-4. | * Wimp, Jet, and Doron Zeilberger. 1985. “Resurrecting the Asymptotics of Linear Recurrences.” Journal of Mathematical Analysis and Applications 111 (1) (October): 162–176. doi:10.1016/0022-247X(85)90209-4. | ||
[[분류:수열]] | [[분류:수열]] | ||
2015년 12월 22일 (화) 21:43 판
개요
- 홀로노믹 수열 (P-recursive,P-finite 또는 D-finite이라고도 불림)
- 다음의 형태의 점화식
$$ c_k(n)a_{n+k}+c_{k-1}(n)a_{n+k-1}+\cdots+c_{0}(n)a_{n}=0 \label{lin} $$ 여기서 $c_0,\cdots, c_k\neq 0$는 $n$의 다항식
예
- 팩토리얼(factorial), $a_n=n!$
$$ a_{n+1}-(n+1)a_n=0 $$
$$ (n+2)a_{n+1}+(-4 n-2)a_{n}=0 $$
$$ n^2 u_{n}-(11n^2-11n+3)u_{n-1}-(n-1)^2u_{n-2}=0 \label{z2} $$
매스매티카 파일 및 계산 리소스
- https://docs.google.com/file/d/0B8XXo8Tve1cxRjVVZU9kYTRMeFE/edit
- http://www.wolfram.com/products/mathematica/newin7/content/NewNumberTheoryCapabilities/WorkWithHolonomicSequences.html
리뷰, 에세이, 강의노트
- Koepf, Wolfram. 1997. “The Algebra of Holonomic Equations.” Mathematische Semesterberichte 44 (2): 173–194. doi:10.1007/s005910050032. http://www.mathematik.uni-kassel.de/~koepf/Publikationen/Algebra.pdf
- Some properties of holonomic sequences
관련논문
- Ekhad, Shalosh B., and Doron Zeilberger. “The C-Finite Ansatz Meets the Holonomic Ansatz.” arXiv:1512.06902 [math], December 21, 2015. http://arxiv.org/abs/1512.06902.
- Wimp, Jet, and Doron Zeilberger. 1985. “Resurrecting the Asymptotics of Linear Recurrences.” Journal of Mathematical Analysis and Applications 111 (1) (October): 162–176. doi:10.1016/0022-247X(85)90209-4.