On a product of modified Bessel functions

Author:
Árpád Baricz

Journal:
Proc. Amer. Math. Soc. **137** (2009), 189-193

MSC (2000):
Primary 33C10, 33C15

Published electronically:
August 1, 2008

MathSciNet review:
2439440

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Abstract: Let and denote the modified Bessel functions of the first and second kinds of order In this note we prove that the monotonicity of on for all is an almost immediate consequence of the corresponding Turán type inequalities for the modified Bessel functions of the first and second kinds of order Moreover, we show that the function is strictly completely monotonic on for all At the end of this note, a conjecture is stated.

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Additional Information

**Árpád Baricz**

Affiliation:
Faculty of Economics, Babeş-Bolyai University, RO-400591 Cluj-Napoca, Romania

Email:
bariczocsi@yahoo.com

DOI:
https://doi.org/10.1090/S0002-9939-08-09571-3

Keywords:
Modified Bessel functions,
complete monotonicity,
Tur\'an type inequalities.

Received by editor(s):
December 13, 2007

Published electronically:
August 1, 2008

Additional Notes:
This research was partially supported by the Institute of Mathematics, University of Debrecen, Hungary

Dedicated:
Dedicated to my son Koppány

Communicated by:
Carmen C. Chicone

Article copyright:
© Copyright 2008
American Mathematical Society