## Is the Euler-Mclaurin sum formula valid for distributions ?

If we take the Euler MacLaurin sum formula

$$\int_{a}^{b} dxf(x) - \sum_{n=a} ^{b}f(n)= (1/2)(f(b)+f(a))+ \sum_{r}B_{2r}(2n!)^{-1}D^{2r-1}(f(b)-f(a))$$

However let's suppose that f(x) or the first , third , ... derivative is just for example a Dirac delta distribution or $$D^{k}\delta (x-c)$$

We could use distribution theory to justify the derivative of a Dirac delta, so the Euler Mac Laurin sum formula would yied to distribution instead of real valued function but i am not sure.

to put an example, let suppose that f(x) is proportional to the floor function $$floor|x^2 + 3|$$ so its first derivative is just a Dirac delta.
 PhysOrg.com science news on PhysOrg.com >> City-life changes blackbird personalities, study shows>> Origins of 'The Hoff' crab revealed (w/ Video)>> Older males make better fathers: Mature male beetles work harder, care less about female infidelity

 Similar discussions for: Is the Euler-Mclaurin sum formula valid for distributions ? Thread Forum Replies General Math 12 Calculus 0 Differential Equations 14 Calculus 0 General Math 9