Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind

Title: Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind
Creator: Borwein, J. M.; Zucker, I. J.
Relation: IMA Journal of Numerical Analysis Vol. 12, Issue 4, p. 519-526
Publisher Link: http://dx.doi.org/10.1093/imanum/12.4.519
Publisher: Oxford University Press
Resource Type: journal article
Date: 1992
Description: Much simplified expressions for certain complete elliptic integrals in terms of the beta function are produced. The reverse procedure of expressing gamma functions in terms of complete elliptic integrals allows us to use the arithmetic-geometric mean iteration to compute gamma functions, using quadratically convergent iterations. Explicit algorithms are given for computing ≤(n/4) and ≤(n/6), where 1≤m≤3 and 1≤n≤5.
Subject: elliptic integrals; gamma functions; arithmetic geometric mean iteration; quadratically convergent iterations
Identifier: http://hdl.handle.net/1959.13/940989
Identifier: uon:13147
Identifier: ISSN:0272-4979
Language: eng
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