  We prove a functional equation for the three-variable $p$-adic $L$-function
attached to the Rankin-Selberg convolution of a Coleman family and a CM Hida
family, which was studied by Loeffler and Zerbes. Consequentially, we deduce
that an anticyclotomic $p$-adic $L$-function attached to a $p$-non-ordinary
modular form vanishes identically in the indefinite setting.

Number Theory