论文标题
在计算过度分区函数的非线性关系上
On a nonlinear relation for computing the overpartition function
论文作者
论文摘要
1939年，H。S。Zuckerman提供了一个Hardy-Ramanujan-Rademacher型收敛系列，该系列可用于计算过度分类函数$ \ OVERLINE {p}（n）$的隔离值。通过这种方法计算$ \叠加{p}（n）$需要算术，具有非常高精度的近似实数，并且很复杂。在本文中，我们提供了一个公式来计算$ \ overline {p}（n）$的值，该值仅需要$ \ overline {p}（k）$的值，其中$ k \ leqslant n/2 $。该公式与多分会函数$ \ OVILLINE {p}（n）$的已知线性均匀复发关系结合使用，以获得$ \ overline {p}（n）$的简单快速计算。该新方法仅使用（大）整数算术，并且更简单地编程。
In 1939, H. S. Zuckerman provided a Hardy-Ramanujan-Rademacher-type convergent series that can be used to compute an isolated value of the overpartition function $\overline{p}(n)$. Computing $\overline{p}(n)$ by this method requires arithmetic with very high-precision approximate real numbers and it is complicated. In this paper, we provide a formula to compute the values of $\overline{p}(n)$ that requires only the values of $\overline{p}(k)$ with $k\leqslant n/2$. This formula is combined with a known linear homogeneous recurrence relation for the overpartition function $\overline{p}(n)$ to obtain a simple and fast computation of the value of $\overline{p}(n)$. This new method uses only (large) integer arithmetic and it is simpler to program.
