$S$-matrix element of two R-R and one NS states

We explicitly calculate the disk-level $S$-matrix element of two closed string R-R and one open string NS vertex operators in RNS formalism. We show that the amplitude satisfies various duality Ward identities. In particular, when one of the R-R is zero form, the other one is two form, and the NS state is a gauge boson, the amplitude transforms under an S-duality Ward identity to the amplitude of one dilaton, one B-field, and one gauge boson, which has recently been calculated explicitly. We have also proposed a soft theorem for the disk-level scattering amplitude of an ar bitrary number of hard closed strings and one soft open string at the leading order of soft momentum, and we have shown that the above amplitude satisfies the soft theorem.