Statistics

   

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.

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

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