Kullback–Leibler divergence between two Wishart distributions

Question

The result is shown in:

[1] W.D. Penny, KL-Divergences of Normal, Gamma, Dirichlet, and Wishart densities, Available at: www.fil.ion.ucl.ac.uk/~wpenny/publications/densities.ps

But could anyone help me out to understand the lines on top of page 3:

$L=\int \log(\Gamma) Wishart(\Gamma|a,B) d\Gamma$ $=\log(\tilde\Gamma(a,B))$ $=\sum\limits_{i=1}^{d}\Psi((a_{s}+1-i)/2)-\log|B_{s}|+d\log(2)$

($\Psi(.)$ is digamma function)

So what is $\tilde\Gamma(a,B),a_{s},B_{s}$?

Answer 1

I think it's a typo and $a_s = a, B_s = B$. I don't know what the $\tilde\Gamma$ notation is supposed to represent.

If you set it this way, this is consistent with the equations at http://people.ee.duke.edu/~shji/papers/AL_TPAMI.pdf on page 25.