  A simple integral formula as an iterated residue is presented for the
Baker-Akhiezer function related to $A_n$ type root system both in the rational
and trigonometric cases. We present also a formula for the Baker-Akhiezer
function as a Selberg-type integral and generalise it to the deformed
$A_{n,1}$-case. These formulas can be interpreted as new cases of explicit
evaluation of Selberg-type integrals.
