论文标题
一种递归算法，可有效，准确地计算不完整的贝塞尔功能
A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions
论文作者
论文摘要
在先前的工作中，我们开发了一种用于计算不完整Bessel函数的算法，该算法是基于$ g_ {n}^{（1）} $ transformation和slevinsky-safouhi公式的数字挑战。在目前的贡献中，我们通过开发分子序列的复发关系和分母序列，其比率形成近似值的序列，从而改善了该现有的算法，用于不完整的贝塞尔函数。通过找到此复发关系，我们将复杂性从$ {\ cal o}（n^4）$降低到$ {\ cal o}（n）$。我们绘制相对误差，表明该算法能够用于不完整的贝塞尔功能的精度极高。
In a previous work, we developed an algorithm for the computation of incomplete Bessel functions, which pose as a numerical challenge, based on the $G_{n}^{(1)}$ transformation and Slevinsky-Safouhi formula for differentiation. In the present contribution, we improve this existing algorithm for incomplete Bessel functions by developing a recurrence relation for the numerator sequence and the denominator sequence whose ratio forms the sequence of approximations. By finding this recurrence relation, we reduce the complexity from ${\cal O}(n^4)$ to ${\cal O}(n)$. We plot relative error showing that the algorithm is capable of extremely high accuracy for incomplete Bessel functions.
