Numerical Representations of the Incomplete Gamma Function of Complex-Valued Argument

  title={Numerical Representations of the Incomplete Gamma Function of Complex-Valued Argument},
  author={R. Mathar},
  journal={Numerical Algorithms},
  • R. Mathar
  • Published 2004
  • Mathematics, Computer Science
  • Numerical Algorithms
Various approaches to the numerical representation of the incomplete Gamma function γ(m+1/2,z) for complex arguments z and non-negative small integer indices m are compared with respect to numerical fitness (accuracy and speed). We consider power series, Laurent series, classical numerical methods of sampling the basic integral representation, and others not yet covered by the literature. The most suitable scheme is the construction of Taylor expansions around nodes of a regular, fixed grid in… Expand
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