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

10.1016/j.jmaa.2008.08.024

Richards, Kendall C.

2018-02-27

2018-02-27

2009

Barnard, R. W., Gordy, M. B., & Richards, K. C. (January 01, 2009). A note on Turán type and mean inequalities for the Kummer function. Journal of Mathematical Analysis and Applications, 349, 1, 259-263.

https://collections.southwestern.edu/s/suscholar/item/238

Turán-type inequalities for combinations of Kummer functions involving Φ(a ± ν, c ± ν, x)
and Φ(a, c ± ν, x) have been recently investigated in [Á. 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 Turán-type and closely related mean inequalities for the additional case involving Φ(a ± ν, c, x). The application to modeling credit risk is also summarized.

English

Journal of Mathematical Analysis and Applications

Kummer confluent hypergeometric function

Turán-type inequality

Mean

Generalized hypergeometric function

Article