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The Ehrhart function for symbols and a generalization of Eulers constant. Ehrhart from Euler- MacLaurin. Simple and non-simple polytopes. Non-simple Simple Some references for the exact Euler-MacLaurin formula in higher dimensions.

  1. The Ehrhart function for symbols and a generalization of Euler’s constant.

  5. Ehrhart from Euler- MacLaurin.

  6. Simple and non-simple polytopes. Non-simple Simple

  7. Some references for the exact Euler-MacLaurin formula in higher dimensions.

  8. Regular polytopes.

  9. Regular and non- regular polytopes.

  10. The Khovanskii- Pukhlikov formula, 1.

  11. The Khovanskii- Pukhlikov formula, 2, moving the facets.

  12. The Khovanskii- Pukhlikov formula,3, the Todd operator.

  13. The Khovanskii- Pukhlikov formula.

  14. Symbols.

  15. Polyhomogeneous symbols. n

  16. The order of a symbol.

  17. The Ehrhart formula.

  19. The constant C .

  21. Independence of regularization.

  23. The polar decomposition theorem.

  26. The construction in general.

  27. Polar decomposition.

  29. Using unweighted sums.

  30. The Euler-MacLaurin formula with remainder.

  33. A very rough outline of the proof.

  34. The limiting form of the remainder.

  44. Relation to Euler’s gamma.

  46. Relation of C(s) to the zeta function.

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