1) homogeneous linear recurrent sequence of number
齐次线性递归数列
1.
This article provides the sufficient condition of how to judge if a sequence of number is a homogeneous linear recurrent sequence of number according to the formula of general term,and the structure of its recursive equation.
给出并证明了由数列的通项公式判定其是齐次线性递归数列的充分条件,以及其递归方程的构造。
2) Invariable coefficient the number of times is different linear recursion sequence
常系数非齐次线性递归数列
1.
Invariable coefficient the number of times is different linear recursion sequence will transform using the sequence difference as often the coefficient inhomogeneous linear difference equation,Thus obtains one kind of computation Invariable coefficient the number of times is different linear recursion sequence special another interpretation simple method.
利用数列的差分将常系数非齐次线性递归数列转化为常系数非齐次线性差分方程,从而得到一种求常系数非齐次线性递归数列特解的简易方法。
3) nd order linear constant coefficient progressive regression equation
二阶线性常系数齐次递归式
4) Linear homogeneous recursion equation with constant coefficient
常系数线性齐次递归方程
5) linear non-homogeneous recursion equation with constant coefficient
常系数线性非齐次递归方程
1.
We give a theoretical basis for special solution of the linear non-homogeneous recursion equation with constant coefficient.
给出了一般求常系数线性非齐次递归方程特解的理论依据。
6) nonhom ogeneous linear recurrence equation
非齐次线性递归方程
1.
A form ula fora specialsolution to nonhom ogeneous linear recurrence equations w ith constant coefficients is derived from a generalorder-reducing form ula presented here.
提出了非齐次线性递归方程的降阶公式,并由此导出了常系数非齐次线性递归方程的特解公式。
补充资料：递归数列
| 递归数列 recursive sequence 一种用归纳方法给定的数列。例如，等比数列可以用归纳方法来定义，先定义第一项a1的值(a1≠0)，对于以后的项，用递推公式an+1＝qan（q≠0，n＝1，2，…）给出定义。一般地，递归数列的前k项a1，a2，…，ak为已知数，从第k＋1项起，由某一递推公式an+k＝f（an，an+1，…，an+k-1）( n＝1，2，…）所确定。k称为递归数列的阶数。例如 ，已知 a1＝1，a2＝1，其余各项由公式an+1＝an＋an-1（n＝2，3，…）给定的数列是二阶递归数列。这是斐波那契数列，各项依次为 1，1，2，3，5，8，13，21，…，同样，由递归式an+1－an ＝an－an-1( a1，a2为已知，n＝2，3，… ) 给定的数列，也是二阶递归数列，这是等差数列。 |
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参考词条