擅长:python、mysql、java
<p>为了得到有理形式母函数<code>a_n</code>的一般公式,可以使用SymPy的<a href="https://docs.sympy.org/latest/modules/series/formal.html#rational-algorithm" rel="nofollow noreferrer">^{<cd2>}</a>。
例如:</p>
<pre class="lang-py prettyprint-override"><code>from sympy import simplify
from sympy.abc import x, n
from sympy.series.formal import rational_algorithm
f = (5*x + 3)/(1-x**2)
func_n, independent_term, order = rational_algorithm(f, x, n, full=True)
print(f"The general formula for a_n is {func_n}")
for k in range(10):
print(f"a_{k} = {simplify(func_n.subs(n, k))}")
</code></pre>
<p>输出:</p>
<pre><code>The general formula for a_n is (-1)**(-n - 1) + 4
a_0 = 3
a_1 = 5
a_2 = 3
a_3 = 5
a_4 = 3
a_5 = 5
a_6 = 3
a_7 = 5
a_8 = 3
a_9 = 5
</code></pre>