This work is an extension of previous work by Alazah et al. [M. Alazah, S. N. Chandler-Wilde, and S. La Porte, Numerische Mathematik, 128(4):635-661, 2014]. We split the computation of the Fresnel Integrals into 3 cases: a truncated Taylor series, modified trapezoid rule and an asymptotic expansion for small, medium and large arguments respectively. These special functions can be computed accurately and efficiently up to an arbitrary precision. Error estimates are provided and we give a systematic method in choosing the various parameters for a desired precision. We illustrate this method and verify numerically using double precision.

中文翻译：

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菲涅耳积分计算技术

这项工作是对Alazah等人先前工作的扩展。[M. Alazah，SN Chandler-Wilde和S.La Porte，Numerische Mathematik，128（4）：635-661，2014]。我们将菲涅耳积分的计算分为3种情况：截断的泰勒级数，修改的梯形规则和分别针对小，中和大参数的渐近展开。可以精确有效地计算这些特殊功能，达到任意精度。提供了误差估计，我们提供了一种系统的方法来选择各种参数以获得所需的精度。我们说明了这种方法，并使用双精度数值验证。