Suppose that U has an F distribution with ν1 and ν2 degrees of freedom. It is well known that as ν2 approaches infinity, the limiting distribution of ν1U is chi-square with ν1 degrees of freedom.
@article{urn:eudml:doc:40685, title = {On a property of the F distribution.}, journal = {Trabajos de Estad\'\i stica e Investigaci\'on Operativa}, volume = {33}, year = {1982}, pages = {110-111}, language = {en}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:40685} }
Crofts Jr., Alfred E. On a property of the F distribution.. Trabajos de Estadística e Investigación Operativa, Tome 33 (1982) pp. 110-111. http://gdmltest.u-ga.fr/item/urn:eudml:doc:40685/