About an extension of the Matsumoto-Yor property

Gérard Letac, Jacek Wesołowski

If $\alpha ,\beta >0$ are distinct and if $A$ and $B$ are independent non-degenerate positive random variables such that $$S=\tfrac{1}{B}\,\tfrac{βA+B}{αA+B}\quad \mbox{and}\quad T=\tfrac{1}{…