The Rogers-Ramanujan-Gordon theorem for overpartitions

Let B-k,B- i(n) be the number of partitions of n with certain difference condition and let A(k, i)(n) be the number of partitions of n with certain congruence condition. The Rogers-Ramanujan-Gordon theorem states that B-k,B- i(n)=A(k, i)(n). Lovejoy obtained an overpartition analogue of the Rogers-Ramanujan-Gordon theorem for the cases i=1 and i=k. We find an overpartition analogue of the Rogers-Ramanujan-Gordon theorem in the general case. Let D-k,D- i(n) be the number of overpartitions of n satisfying certain difference condition and C-k,C- i(n) be the number of overpartitions of n whose non-overlined parts satisfy certain congruence condition. We show that C-k,C- i(n)=D-k,D- i(n). By using a function introduced by Andrews, we obtain a recurrence relation that implies that the generating function of D-k,D- i(n) equals the generating function of C-k,C- i(n). By introducing the Gordon marking of an overpartition, we find a generating function formula for D-k,D- i(n) that can be considered an overpartition analogue of an identity of Andrews for ordinary partitions.