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：本文探讨利用Gauss-Laguerre公式计算Lerch超越函数的方法。文中推导了求积误差的先验估计式，该估计式可计算达到任意精度所需的求积节点数。通过利用Gauss-Laguerre规则与误差估计的性质，本文还提出了一种截断方法。给出了所用算法及其Matlab实现。数值算例验证了该方法的可靠性。