一类Hausdorff变换幂级数的Watson重求和
Watson resummation of a class of Hausdorff-transformed power series
AI总结：
针对一类收敛极慢的Hausdorff变换幂级数，利用Pollaczek多项式进行Watson型重求和，得到收敛更快的表示，并提出数值计算新算法，同时解决经典Hausdorff矩问题。
摘要：
本文研究了一类Hausdorff变换幂级数，其对于大的自变量值收敛极慢。我们对这些展开进行了Watson型重求和，并利用Pollaczek多项式得到了一个收敛更快的新的表示。因此，我们可以提出一种新的数值计算这些展开的算法，这些展开包括在统计力学中计算配分函数时起重要作用的级数。通过同样的过程，我们还得到了经典Hausdorff矩问题的一个解。
英文摘要：
In this paper we study a class of Hausdorff--transformed power series whose convergence is extremely slow for large values of the argument. We perform a Watson-type resummation of these expansions, and obtain, by the use of the Pollaczek polynomials, a new representation whose convergence is much faster. We can thus propose a new algorithm for the numerical evaluation of these expansions, which include series playing a relevant role in the computation of the partition function in statistical mechanics. By the same procedure we obtain also a solution of the classical Hausdorff moment problem.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
