### Special Function Invocation

O Hive Mind, o Lazy Web, Urania's child, I invoke thee! Is there a name
for the function
\[
f_n(\theta) = \sum_{k=0}^{n}{{n \choose k} \theta^k {(1-\theta)}^{n-k} \log{k!}}
\]
i.e., for \( \mathbb{E}[\log{X!}] \) when \( X \) is binomially distributed?

Enigmas of Chance

Posted at March 22, 2009 21:52 | permanent link