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

Baker-Akhiezer function as iterated residue and Selberg-type integral