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Topic: 1/trigamma(x) : Convex function ?
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Posts: 6
Registered: 7/24/07
1/trigamma(x) : Convex function ?
Posted: Jul 18, 2012 3:24 AM
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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?


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