Register to reply

Is the Euler-Mclaurin sum formula valid for distributions ?

Share this thread:
mhill
#1
Feb2-08, 05:16 AM
P: 193
If we take the Euler MacLaurin sum formula

[tex] \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)) [/tex]

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

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 [tex] floor|x^2 + 3| [/tex] so its first derivative is just a Dirac delta.
Phys.Org News Partner Science news on Phys.org
New type of solar concentrator desn't block the view
Researchers demonstrate ultra low-field nuclear magnetic resonance using Earth's magnetic field
Asian inventions dominate energy storage systems

Register to reply

Related Discussions
The Cramer-Euler-McLaurin Paradox General Math 12
Euler-Mc laurin sum formula wit dilation. Calculus 0
Results same w/ Euler, Improved Euler, & Runge-Kutta Differential Equations 14
Abel sum formula..when is valid?.. Calculus 0
Is this a valid limit? General Math 9