A note on Turan type and mean inequalities for the Kummer function

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:349

Article

Barnard, Roger W.²  Gordy, Michael B.³  Richards, Kendall C.¹ 

[1] Southwestern Univ, Dept Math, Georgetown, TX 78627 USA

[2] Texas Tech Univ, Dept Math, Lubbock, TX 79409 USA

[3] Fed Reserve Board, Div Res & Stat, Washington, DC 20551 USA

关键词: Kummer confluent hypergeometric function;    Turan-type inequality;    Mean;    Generalized hypergeometric function;   

DOI  :  10.1016/j.jmaa.2008.08.024

来源: Elsevier

【 摘 要 】

Turan-type inequalities for combinations of Kummer functions involving Phi(a +/- v, c +/- v.x) and Phi(a.c +/- v.x) have been recently investigated in [A. Baricz, Functional inequalities involving Bessel and modified Bessel functions of the first kind, Expo. Math. 26 (3) (2008) 279-293: M.E.H. Ismail, A. Laforgia. Monotonicity properties of determinants of special functions, Constr. Approx. 26 (2007) 1-9]. In the current paper, we resolve the corresponding Turin-type and closely related mean inequalities for the additional case involving (P (a v, c, x). The application to modeling credit risk is also summarized. (C) 2008 Elsevier Inc. All rights reserved.

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