On Ruijsenaars' asymptotic expansion of the logarithm of the double gamma function
Ημερομηνία
2008ISSN
0022-247XSource
Journal of Mathematical Analysis and ApplicationsVolume
341Issue
2Pages
1125-1132Google Scholar check
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Εμφάνιση πλήρους εγγραφήςΕπιτομή
We study the remainder RN (x) in an asymptotic expansion due to S.N.M. Ruijsenaars, for the logarithm of the double gamma function. We show that for any even number N the function (- 1)frac(N, 2) - 1 RN (x) is completely monotonic on (0, ∞). This proves a recent conjecture of H.L. Pedersen. In addition, we give an estimate for the remainder RN (x) for N even. © 2007 Elsevier Inc. All rights reserved.