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Taylor Transform
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Jon Slaughter
Jun 5, 2009, 9:26:39 PM6/5/09
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If we extend the taylor series from the discrete to continuous by
g(x) = int(f(t)*x^t/Gamma(t+1),t=0..oo) we get some type of integral
transform(although not sure if it is invertible).
Is this "known" and used?
Martin Musatov
Jun 5, 2009, 10:49:38 PM6/5/09
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https://share.acrobat.com/adc/adc.do?docid=80c126dd-8961-4a57-9351-22abcd68de3b
It is applied in this legitimate NP_Complete application. Challengers
note whether responses address mathematic specifics:
http://scottaaronson.com/blog/?p=406
++
Martin Musatov
Los Angeles, CA
rancid moth
Jun 9, 2009, 2:04:02 AM6/9/09
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I think it's just the Mellin transform, except you have taken
f(t)/Gamma(t+1) instead of f(t). and you are taking -t instead of t so you
need to look carefully at what happens to the fundamental strip when it
comes to inversion.
Richard L. Peterson
Nov 21, 2009, 2:26:31 AM11/21/09
to
It's something I wondered about too.
A few years ago I saw the following
by Jonathan P. Dowling:"The Mathematics
of the Casimir Effect" in MATHEMATICS
MAGAZINE December 1989 page 324, vol 62,
no. 5.
It is true the title doesn't sound relevant,
but the article discusses some of your
ideas.
Hope this is helpful.
A few years ago I saw the following
by Jonathan P. Dowling:"The Mathematics
of the Casimir Effect" in MATHEMATICS
MAGAZINE December 1989 page 324, vol 62,
no. 5.
It is true the title doesn't sound relevant,
but the article discusses some of your
ideas.
Hope this is helpful.
Richard L. Peterson
Nov 21, 2009, 10:48:25 PM11/21/09
to
when i fiddled with it, in the nineties, i
did stuff like int[x^ndn]=-1/ln(x),
vs. sum[x^n] = 1/(1-x); provided in both x
is in (0,1) and n is integrated or summed
from 0 to infinity. i also tried things
like int{[(e^x)/n!]dn} with n! interpreted
as you have as gamma(n+1), but i don't recall
getting very far, just plotting some points.
did stuff like int[x^ndn]=-1/ln(x),
vs. sum[x^n] = 1/(1-x); provided in both x
is in (0,1) and n is integrated or summed
from 0 to infinity. i also tried things
like int{[(e^x)/n!]dn} with n! interpreted
as you have as gamma(n+1), but i don't recall
getting very far, just plotting some points.
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