A stable recurrence for the incomplete gamma function with imaginary second argument

@article{Deun2006ASR,
  title={A stable recurrence for the incomplete gamma function with imaginary second argument},
  author={J. V. Deun and R. Cools},
  journal={Numerische Mathematik},
  year={2006},
  volume={104},
  pages={445-456}
}
Even though the two term recurrence relation satisfied by the incomplete gamma function is asymptotically stable in at least one direction, for an imaginary second argument there can be a considerable loss of correct digits before stability sets in. We present an approach to compute the recurrence relation to full precision, also for small values of the arguments, when the first argument is negative and the second one is purely imaginary. A detailed analysis shows that this approach works well… Expand

References

SHOWING 1-10 OF 30 REFERENCES
An asymptotic representation for the Riemann zeta function on the critical line
  • R. Paris
  • Mathematics
  • Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
  • 1994
Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
The asymptotic expansion of the incomplete gamma functions : (preprint)
The generalized exponential integral
A Matlab Implementation of an Algorithm for Computing Integrals of Products of Bessel Functions
Uniform asymptotic smoothing of Stokes’s discontinuities
  • M. Berry
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
  • 1989
...
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2
3
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