  In this paper, we generalize two results of H. Darmon and V. Rotger on triple
product $p$-adic $L$-functions associated with Hida families to finite slope
families. We first prove a $p$-adic Gross-Zagier formula, then demonstrate an
application to a special case of the equivariant Birch and Swinnerton-Dyer
conjecture for supersingular elliptic curves.
