论文标题
先验解决方案对线性系数非均匀二阶复发关系，持续非疫苗
Transcendental solution to linear coefficient non-homogeneous second order recurrence relation with constant non-homogenity
论文作者
论文摘要
实数的二阶复发关系在离散的时间动态系统以及马尔可夫链上的上下文中形成了各种应用。复发关系的解决方案由前两个初始值以及复发公式充分定义。我们在这项工作中明确地计算出$ a_1 $的最低阳性解决方案$（a_i）_ {i \ in \ mathbb {n}} $ to非均匀的二阶恢复关系，而当非均匀性是恒定和负值时，并且第一个初始值是恒定的，并且第一个初始值是持续的，并且是第一个初始值等于$ a_0 $ a_0 $ a_0 $ a_0 = 0.0 = 0 = 0。我们表明，有理系数导致一系列先验数。此外，我们证明，当改变$ a_1 $，收敛到$ 0 $并获得$ o（i^{ - 1}）$时，该序列是唯一有限的解决方案。我们在上一节中进一步评论了复发关系中有理参数的选择，并链接到不可能获得基于计算机的最小阳性解决方案的可视化$（a_i）_ {i \ in \ mathbb {n}} $。
Second order recurrence relations of real numbers arise form various applications in discrete time dynamical systems as well as in the context on Markov chains. Solutions to the recurrence relations are fully defined by the first two initial values as well as the recurrence formula. We calculate in this work explicitly as a function of $a_1$ the minimal positive solution $(a_i)_{i\in\mathbb{N}}$ to non-homogeneous second order recurrence relation with affine coefficients when the non-homogeneity is constant and negative, and the first initial value equals $a_0=0$. We show that rational coefficients lead to a sequence of transcendental numbers. Additionally, we prove that this sequence is the only bounded solution when varying $a_1$, converges to $0$ and obtain the convergence speed in $O(i^{-1})$. We comment in the last section further on the choice of rational parameters in the recurrence relation and we make a link to the impossibility of obtaining computer based visualizations of the minimal positive solution $(a_i)_{i\in\mathbb{N}}$.
