I'm using the Euler-Maclaurin formula in a research I'm working on. However brilliant is the elementary proof found [here][1], I need and want to know more about it. Namely

 1. Generalizations to broader function spaces then the analytic functions 
 2. Generalizations to Lebesgue integrals with respect to other measures.
 3. Reminder theorems for continuously differentiable functions.

Most of what I've found were either research papers, or citation of a convenient formula for a specific application. I'm looking for good reviews or textbook chapters which focus on the formula itself.

Thanks

Amir

  [1]: http://www.jstor.org/stable/2589145?seq=1#page_scan_tab_contents