A note on the recursive calculation of incomplete gamma functions

  title={A note on the recursive calculation of incomplete gamma functions},
  author={W. Gautschi},
  journal={ACM Trans. Math. Softw.},
  • W. Gautschi
  • Published 1999
  • Mathematics, Computer Science
  • ACM Trans. Math. Softw.
It is known that the recurrence relation for incomplete gamma functions {γ(<italic>a</italic> + <italic>n</italic>, <italic>x</italic >)}, 0 ≤ <italic>a</italic> < 1, <italic>n</italic> = 0, 1, 2 ..., when <italic>x</italic> is positive, is unstable—more so the larger <italic>x</italic>. Nevertheless, the recursion can be used in the range 0 ≤ <italic>n</italic> ≤ <italic>x</italic> practically without error growth, and in larger ranges 0 ≤ <italic>n</italic> ≤ <italic>N</italic> with a loss of… Expand
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