The Bridgeman-Kahn identity for hyperbolic manifolds with cusped   boundary
  In this note, we extend the Bridgeman-Kahn identity to all finite-volume orientable hyperbolic $n$-manifolds with totally geodesic boundary. In the compact case, Bridgeman and Kahn are able to express the manifold's volume as the sum of a function over only the orthospectrum. For manifolds with non-compact boundary, our extension adds terms corresponding to intrinsic invariants of boundary cusps. 
Nicholas G. Vlamis and Andrew Yarmola
math.GT