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## What is the formulation of the precise Weitzenbock formula ?

E is a holomorphic vector bundle over a complex manifold. I want to calculate the Laplacian of E-valued (p,q) forms.In P100 of Griffith-Harris' book(trivial line bundle case),they mention a "precise Weitzenbock formula".In the previous calculation,they only give the terms of order 2,what is the formulation of the lower order terms?

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Just a brief hint: en.wikipedia.org/wiki/Weitzenb%C3%B6ck_identity – mathphysicist May 17 2011 at 11:00