Alex Herbert created NUMBERS-219:
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Summary: Digamma and Trigamma limits at -infinity are unspecified;
at +infinity are defined
Key: NUMBERS-219
URL: https://issues.apache.org/jira/browse/NUMBERS-219
Project: Commons Numbers
Issue Type: Improvement
Components: gamma
Affects Versions: 1.0
Reporter: Alex Herbert
The Digamma and Trigamma functions currently return the input argument if it is
not finite. NaN is returned as NaN and infinity is returned as the same
infinity. These infinite limits are not correct.
||Function||Argument||Limit||Return||
|Digamma|-infinity|Has infinite poles at integer values. As x moves toward
negative infinity along the real axis, it repeatedly crosses these infinite
poles and oscillates between + and - infinity. The value diverges and has no
limit.|NaN|
|Digamma|infinity|The function grows (logarithmically) without bound to
infinity|infinity|
|Trigamma|-infinity|As for the digamma function, the real-valued trigamma
function features infinite poles at all non-positive integers. Between these
poles it oscillates and does not have a simple limit.|NaN|
|Trigamma|infinity|The function decays asymptotically like 1 / x towards
zero.|0|
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