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The definition of Stirling numbers for complex arguments proposed by Flajolet & Prodinger is studied. Stirling numbers are defined by contour integrals in the complex plane. In addition to symbolic special cases, methods for evaluating the integrals numerically are presented. Numerical integration methods based on exponentially convergent trapezoidal schemes are implemented; optimizations of the calculations are explored.

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Computation of Stirling Numbers for Complex Arguments

  • 会议论文

  • 发表日期：

    2026年

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  • Robert M. Corless,
  • David J. Jeffrey,
  • Qingze Li

摘要

The definition of Stirling numbers for complex arguments proposed by Flajolet & Prodinger is studied. Stirling numbers are defined by contour integrals in the complex plane. In addition to symbolic special cases, methods for evaluating the integrals numerically are presented. Numerical integration methods based on exponentially convergent trapezoidal schemes are implemented; optimizations of the calculations are explored.