Schur multiple zeta-functions of Hurwitz type

We study the Hurwitz-type analogue of Schur multiple zeta-functions involving shifting parameters. We extend various formulas, known for ordinary Schur multiple zeta-functions, to the case of Hurwitz type. We also mention unpublished results proved by Yamamoto and by Minoguchi. Further we present new formulas obtained by performing differentiation with respect to shifting parameters.