I show a simple expression of the Mill's ratio of the Student's t-Distribution. I use it to prove Conjecture 1 in P. Auer, N. Cesa-Bianchi, and P. Fischer.

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Abstract

I show a simple expression of the Mill's ratio of the Student's
t-Distribution. I use it to prove Conjecture 1 in P. Auer, N. Cesa-Bianchi, and
P. Fischer. Finite-time analysis of the multiarmed bandit problem. Mach.
Learn., 47(2-3):235--256, May 2002.