  After reviewing some fundamental facts from the theory of theta
hypergeometric series we derive, using indefinite summation, several summation,
transformation, and expansion formulas for multibasic theta hypergeometric
series. Some of the identities presented here generalize corresponding formulas
given in Chapter 11 of the Gasper and Rahman book [Basic hypergeometric series,
2nd ed., Encyclopedia of Mathematics And Its Applications 96, Cambridge
University Press, Cambridge, 2004].
