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Powerful way to perform continuum sum
#8
I'm a little confused about what you're doing but I understand your arguments about sexp as a continuum product.


We have A beautiful result I would like to show:

We start with the two identities that are already proven by others working on fractional calculus.





And even more generally:


whree the convolution is done over s, and the values at t are the same for both f and g.

Therefore: if and



That means even more remarkably



That means

This has so much value for continuum sums. This is remarkable!

I have to properly justify this using the continuity of these operators over some hilbert space. That's the only way I can think of.



I would also like to standardize a notation that is very intuitive. If we take the continuum sum over the interval [a,b] we say:



This has all the linearity rules of the integral, and some own unique rules of its own.

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Messages In This Thread
Powerful way to perform continuum sum - by JmsNxn - 08/10/2013, 09:06 PM
RE: Powerful way to perform continuum sum - by JmsNxn - 08/12/2013, 07:17 PM

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