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GeorgeK
Posts:
6
Registered:
7/24/07


1/trigamma(x) : Convex function ?
Posted:
Jul 18, 2012 3:24 AM


Hello,
I am trying to show that:
1/trigamma(m+n) > 1/trigamma(m) + 1/trigamma(n)
which is easy if I can show that 1/trigamma(x) is convex. This seems to be the case on a graphical representation, but not so easy as I thought to demonstrate.
If I calculate the second derivative of 1/trigamma(x), it would be positive if:
2*[tetragamma(x)^2]pentagamma(x)trigamma(x) > 0
but I don't know what to do with that :(
Any hint?
G.



