The Twisted Doubling Method in Algebraic Families

We define the twisted doubling zeta integrals of Cai-Friedberg-Ginzburg-Kaplan in the setting of algebraic families. We then prove a rationality result and a functional equation for these zeta integrals. This allows us to define an unnormalized $\gamma$-factor associated to certain families of representation of a classical group times a general linear group.