query: What are some basic methods to solve a recursive function of the shape $f_n = \alpha f_{n-1} + \beta f_{n-2}$ where $\alpha, \beta \in\mathbb{R}$
positive_passages.docid: 144890
positive_passages.text: Recurrence $f_{n+2}=af_{n+1}+bf_n$
negative_passages.docid: 29403
negative_passages.text: Finding functions $f: \Bbb R_*^+ \to \Bbb R_*^+$ with certain properties
negative_passages.docid: 42218
negative_passages.text: How to find out the following function f which is a function of r?
negative_passages.docid: 76046
negative_passages.text: Finding the roots of the unknown function
negative_passages.docid: 61592
negative_passages.text: Exponential generating function to find recurrence formula $a_n$
negative_passages.docid: 144260
negative_passages.text: Solve recurrence relation $a_n = 3 a_{n - 3} + a_{n-1} + 2 n$
negative_passages.docid: 70997
negative_passages.text: showing a genereral function from a generating function and recursive function
negative_passages.docid: 81371
negative_passages.text: Solving recurrence $T(n) = T(\lceil n/2 \rceil) + T(\lfloor n/2 \rfloor) + \Theta(n)$
negative_passages.docid: 25984
negative_passages.text: Explicit solution of the recursion $x_n = x_{n-1}^2 - 2$ with $x_0>2$
negative_passages.docid: 150822
negative_passages.text: Finding $\sum_{k=0}^{n-1}\frac{\alpha_k}{2-\alpha_k}$, where $\alpha_k$ are the $n$-th roots of unity
negative_passages.docid: 57071
negative_passages.text: Examples of Recursive functions
negative_passages.docid: 89705
negative_passages.text: How to solve $a_n = 2a_{n-1} + 1, a_0 = 0, a_1 = 1$?
negative_passages.docid: 41409
negative_passages.text: Ackermann Function primitive recursive
negative_passages.docid: 79121
negative_passages.text: How can I build a recursive function in python?
negative_passages.docid: 156778
negative_passages.text: Finding functions satisfying $f(f(x))+f(x)+x=0$
negative_passages.docid: 58088
negative_passages.text: Find recursive formula for sequence $a_n = \left(\frac23\right)^n + n$
negative_passages.docid: 75448
negative_passages.text: Find all function satisfying $f(f(n))+f(n)=2n+3k$