Completely monotonic functions of positive order and asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:355

Article

Koumandos, Stamatis²  Pedersen, Henrik L.¹ 

[1] Univ Copenhagen, Fac Life Sci, Dept Basic Sci & Environm Math & Comp Sci, DK-1871 Frederiksberg C, Denmark

[2] Univ Cyprus, Dept Math & Stat, CY-1678 Nicosia, Cyprus

关键词: Gamma function;    Double gamma function;    Barnes G-function;    Completely monotonic function of positive;    order;    Asymptotic expansion;    Strong complete monotonicity;   

DOI  :  10.1016/j.jmaa.2009.01.042

来源: Elsevier

【 摘 要 】

We introduce completely monotonic functions of order r > 0 and show that the remainders in asymptotic expansions of the logarithm of Barnes double gamma function and Euler's gamma function give rise to completely monotonic functions of any positive integer order. (c) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free