Triple product p-adic L-functions for finite slope families and a p-adic Gross-Zagier formula

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.