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The equivalence of two complete sets of Poisson commuting Hamiltonians of the(super)integrable rational BC(n) Ruijsenaars-Schneider-van Diejen system isestablished. Specifically, the commuting Hamiltonians constructed by van Diejenare shown to be linear combinations of the Hamiltonians generated by thecharacteristic polynomial of the Lax matrix obtained recently by Pusztai, andthe explicit formula of this invertible linear transformation is found.

Equivalence of two sets of Hamiltonians associated with the rational BC(n) Ruijsenaars-Schneider-van Diejen system