This paper deals with the computation of the Lerch transcendent by means of the Gauss-Laguerre formula. An a priori estimate of the quadrature error, that allows to compute the number of quadrature nodes necessary to achieve an arbitrary precision, is derived. Exploiting the properties of the Gauss-Laguerre rule and the error estimate, a truncated approach is also considered. The algorithm used and its Matlab implementation are reported. The numerical examples confirm the reliability of this approach.

翻译：本文件通过高斯-拉盖尔公式处理Lerch 超越值的计算。 推断出对二次差的先验估计, 以便计算达到任意精确度所需的二次点数。 利用高斯- 拉盖尔规则的属性和误差估计, 也考虑一种短线方法。 报告了所使用的算法及其 Matlab 执行。 数字示例证实了这一方法的可靠性 。