We calculate higher-spin Brower-Polchinski-Strassler-Tan (BPST) vertex operators for an open bosonic string and express these operators in terms of a Kummer function of the second kind. We derive an infinite number of recurrence relations among BPST vertex operators of different string states. These recurrence relations among BPST vertex operators lead to the recurrence relations among Regge string scattering amplitudes discovered recently.Note that the convention for s and t adopted here is different from the original BPST paper in Ref. [2].We first review the calculation of tachyon BPST vertex operator [2]. The s À t channel of an open-string fourtachyon amplitude can be written as *