  Since their introduction by Andrews, generalized Frobenius partitions have
interested a number of authors, many of whom have worked out explicit formulas
for their generating functions in specific cases. This has uncovered
interesting combinatorial structure and led to proofs of a number of
congruences. In this paper, we show how Andrews' generating functions can be
cast in the framework of Eichler and Zagier's Jacobi forms. This reformulation
allows us to compute explicit formulas for the generalized Frobenius partition
generating functions (and in fact provides formulas for further functions of
potential combinatorial interest), and it leads to a recursion formula to
calculate them in terms of infinite $q$-products.
