Rational limit of Rains integrals of type A n
The paper derives a rational analogue of elliptic Rains identities by transforming an integral definition using variable replacements and balancing conditions. This method establishes formal pointwise limits connecting elliptic integrals to rational ones, linking them to known integrals like Gustafson and Cauchy determinant identities. It also investigates the commutativity of dual Baxter operators.