Measurements of the branching fractions of semileptonic <i>D_s</i><SUP>+</SUP> decays via <i>e</i><SUP>+</SUP><i>e</i><SUP>-</SUP> → <i>D_s</i>*<SUP>+</SUP><i>D_s</i>*<SUP>-</SUP>

We measure the absolute branching fractions of semileptonic D-s(+), decays via the e(+)e(-) -> D-sD-+(s)(-) process using e(+)e(-) collision data corresponding to an integrated luminosity of 10.64 fb(-1) collected by the BESIII detector at center-of-mass energies between 4237 and 4.699 GeV. The branching fractions are B(D-s(+) -> eta e(+)nu(e)) = (2.35 +/- 0.11(stat) +/- 0.10(syst))%, B(D-s(+) -> eta ' e(+)nu(e)) = (0.82 +/- 0.09(stat) +/- 0.04(syst))%, B(D-s(+) -> phi e(+)nu(e)) = (2.21 +/- 0.16(stat) +/- 0.11(syst))%, B(D-s(+) -> f(0)(980)e(+)nu(e), f(0)(980) -> pi(+)pi(-)) = (0.15 +/- 0.02(stat) +/- 0.01(syst))%, B(D-s(+) -> K(0)e(+)nu(e)) = (0.24 +/- 0.04(stat) +/- 0.01(syst))%, and B(D-s(+) -> K(0)e(+)nu(e)) = (0.19 +/- 0.03(stat) +/- 0.01(syst))%. These results are consistent with those measured via the e(+)e(-) -> D-s*D-+/-(s)-/+ process by BESIII and CLEO. Using two -parameter series expansion, the hadronic transition form factors of D-s(+) -> eta e(+)nu(e), D-s(+) -> eta ' e(+)nu(e) are determined to be f(+)(eta)(0) = 0.442 +/- 0.022(stat) +/- 0.017(sys)t(,) f(+)(eta ')(0) = 0.557 +/- 0.062(stat) +/- 0.024(syst), and f(+)(K0) (0) = 0.677 +/- 0.098(stat) +/- 0.023(syst).