  The extended Heisenberg algebra for a contact manifold has a symbolic
calculus that accommodates both Heisenberg pseudodifferential operators as well
as classical pseudodifferential operators. We derive here a formula for the
index of Fredholm operators in this extended calculus. This formula
incorporates in a single expression the Atiyah-Singer formula for elliptic
operators, as well as Boutet de Monvel's Toeplitz index formula.
