Error Bounds on the Loggamma Function Amenable to Interval Arithmetic

Authors: Russell Leidich

Unlike other common transcendental functions such as log and sine, James Stirling's convergent series for the loggamma (“logΓ”) function suggests no obvious method by which to ascertain meaningful bounds on the error due to truncation after a particular number of terms. (“Convergent” refers to the fact that his original formula appeared to converge, but ultimately diverged.) As such, it remains an anathema to the interval arithmetic algorithms which underlie our confidence in its various numerical applications. Certain error bounds do exist in the literature, but involve branches and procedurally generated rationals which defy straightforward implementation via interval arithmetic. In order to ameliorate this situation, we derive error bounds on the loggamma function which are readily amenable to such methods.

Comments: 13 Pages. This work is licensed under a Creative Commons Attribution 4.0 International License.

Download: PDF

Submission history

[v1] 2016-09-13 11:02:40

Unique-IP document downloads: 33 times is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus