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Let $\Gamma(x)$ be the gamma function and $\Psi(x)$ the digamma function. Define:

$f(x_1,\ldots,x_n) = \sum_{i=1}^n \left( (\Psi(x_i) - \Psi(\sum_i x_i))(c_i - x_i) - \log \Gamma(\sum_i x_i) + \log \Gamma(x_i) \right)$

where $c_i$ are constants.

What is the maximum over $x_i \ge 0$ for this function $f(x)$?

share|cite|improve this question
Why do you need that? – Beni Bogosel Jul 6 '11 at 20:00
it came up during a derivation. – gammer Jul 6 '11 at 20:30

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