The second semi-classical coefficient for Toeplitz operators on strictly pseudoconvex CR manifolds equals e^{-2(n+1)f}((1/2)R_scal + (n+1)Delta_b f) times the integral of chi(t)t^{n-1}dt, divided by (2pi)^{n+1}.
Catlin, The Bergman kernel and a theorem of Tian, Analysis and Geometry in Several Complex Variables, Birkh¨auser, Boston, (1999), pages 1–23
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On the second coefficient in the semi-classical expansion of Toeplitz Operators
The second semi-classical coefficient for Toeplitz operators on strictly pseudoconvex CR manifolds equals e^{-2(n+1)f}((1/2)R_scal + (n+1)Delta_b f) times the integral of chi(t)t^{n-1}dt, divided by (2pi)^{n+1}.