Computing the Incomplete Gamma Function to Arbitrary Precision

@inproceedings{Winitzki2003ComputingTI,
  title={Computing the Incomplete Gamma Function to Arbitrary Precision},
  author={S. Winitzki},
  booktitle={ICCSA},
  year={2003}
}
  • S. Winitzki
  • Published in ICCSA 2003
  • Mathematics, Computer Science
I consider an arbitrary-precision computation of the incomplete Gamma function from the Legendre continued fraction. Using the method of generating functions, I compute the convergence rate of the continued fraction and find a direct estimate of the necessary number of terms. This allows to compare the performance of the continued fraction and of the power series methods. As an application, I show that the incomplete Gamma function Γ (a, z) can be computed to P digits in at most O(P) long… Expand
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A collection of Fortran-90 routines for evaluating the gamma function and related functions using the FM multiple-precision arithmetic package.
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