We use Haff's fundamental identity to express the expectation of Sp in lower-order terms, where S follows the central Wishart distribution.
@article{urn:eudml:doc:42051, title = {A recursion formula for expected negative and positive powers of the central Wishart distribution.}, journal = {SORT}, volume = {31}, year = {2007}, pages = {201-206}, zbl = {1274.62356}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42051} }
Neudecker, Heinz. A recursion formula for expected negative and positive powers of the central Wishart distribution.. SORT, Tome 31 (2007) pp. 201-206. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42051/