| 用升阶法求常系数非齐次线性递推关系的特解 |
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| 引用本文： | 黄纯洁.用升阶法求常系数非齐次线性递推关系的特解[J].茂名学院学报,2011,21(6):67-69,74. |
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| 作者姓名： | 黄纯洁 |
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| 作者单位： | 华南师范大学数学科学学院,广东广州,510631 |
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| 摘 要： | 利用数列的差分算子和移位算子，将常系数非齐次线性递推关系转化成为常系数非齐次线性差分方程（qo△k＋i＋q1△k＋i-1…＋qk△i）an=△if（n），并将f（n）=gm（n），f（n）=qngm（n），f（n）=qngm（n）cosβn，f（n）=qkgm（n）sinβn）这四种类型的常系数非齐次递推关系转化为相应的差分方程，从而得到求常系数非齐次线性递推关系特解的简易方法——升阶法。
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| 关 键 词： | 差分方程 差分算子 移位算子 特解 |
Special Solutions of Constant Coefficient Inhomogeneous Linear Recursion Relation with Rising Order |
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| HUANG Chun-jie.Special Solutions of Constant Coefficient Inhomogeneous Linear Recursion Relation with Rising Order[J].Journal of Maoming College,2011,21(6):67-69,74. |
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| Authors: | HUANG Chun-jie |
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| Institution: | HUANG Chun-jie(College of Mathematics Science,South China Normal University,Guangzhou 510631,China) |
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| Abstract: | This article makes use of the sequence difference, and transforms the invariable coefficient number of times different linear recursion sequence to the coefficient inhomogeneous linear difference equation （ qo （qo△k＋i＋q1△k＋i-1…＋qk△i）an=△if（n）, The fourf（n）=gm（n）,f（n）=qngm（n）,f（n）=qngm（n）cosβn,f（n）=qkgm（n）sinβn） are discussed under constant coefficient inho-mogeneous linear difference equation, thus obtains the special solutions of coefficient inhomogeneous linear recursion sequence, which is called the method of increasing order. |
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| Keywords: | difference equation difference operator displacement operator special solution |
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