@zoranVicovic Please determine a domain for the variables. You are right. The trivial case $x=0$ works, but in general the equation will fail. For example: Let $\alpha=\beta=1$, $x=1$, and $y=2$. The rhs evaluates to $\frac{e-1}{2}$. Exchange x and y ($x=2$, $y=1$) and redo the calculation of the rhs. We get $\frac{e^2-1}{2}$. But looking at the lhs, both values should be the same!

The formula seems to be wrong. The left hand side is symmetric in x and y, but the right hand side is not.