"홀로노믹 수열"의 두 판 사이의 차이

2020년 11월 16일 (월) 04:18 기준 최신판

\[ c_k(n)a_{n+k}+c_{k-1}(n)a_{n+k-1}+\cdots+c_{0}(n)a_{n}=0 \label{lin} \] 여기서 \(c_0,\cdots, c_k\neq 0\)는 \(n\)의 다항식

\[ a_{n+1}-(n+1)a_n=0 \]

\[ (n+2)a_{n+1}+(-4 n-2)a_{n}=0 \]

\[ n^2 u_{n}-(11n^2-11n+3)u_{n-1}-(n-1)^2u_{n-2}=0 \label{z2} \]

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

Jakob Ablinger, Inverse Mellin Transform of Holonomic Sequences, arXiv:1606.02845 [cs.SC], June 09 2016, http://arxiv.org/abs/1606.02845
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.

@@ 2번째 줄: / 2번째 줄: @@
 * 홀로노믹 수열 (P-recursive,P-finite 또는 D-finite이라고도 불림)
 * 다음의 형태의 점화식
-$$
+:<math>
 c_k(n)a_{n+k}+c_{k-1}(n)a_{n+k-1}+\cdots+c_{0}(n)a_{n}=0 \label{lin}
-$$
+</math>
-여기서 $c_0,\cdots, c_k\neq 0$는 $n$의 다항식
+여기서 <math>c_0,\cdots, c_k\neq 0</math>는 <math>n</math>의 다항식
 ==예==
-* [[팩토리얼(factorial)]], $a_n=n!$
+* [[팩토리얼(factorial)]], <math>a_n=n!</math>
-$$
+:<math>
 a_{n+1}-(n+1)a_n=0
-$$
+</math>
 * [[카탈란 수열(Catalan numbers)]]
-$$
+:<math>
 (n+2)a_{n+1}+(-4 n-2)a_{n}=0
-$$
+</math>
 * [[아페리(Apéry) 점화식]]
-$$
+:<math>
 n^2 u_{n}-(11n^2-11n+3)u_{n-1}-(n-1)^2u_{n-2}=0 \label{z2}
-$$
+</math>