| Author |
Comment/Response |
igor igel
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 07/14/12 03:20am
Thank you very much for your previous ideas, the Assumption m1>m0 could be exchanged by m1 and m0 element reals and because of the symmetry b1>b0 was not really a constraint.
Now we need a slighlty different limit: The "geometric mean of the function value of a linear changing gauss function at a specific x value". So before and after we have a gauss function but with different parameters. As the peak of the gauss bell should change linearly, unlike in the previous formula not the standard deviation itself should change linearly but the inverse of it.
Never mind the long story, following limit is searched for:
Limit[prd, n -> Infinity]
prd = Product[(1/\[Sqrt](2 \[Pi]) ((n - i)/(n b0) + i/(n b1)) E^(-1/
2 ((n - i)/n m0 + i/n m1 - x)^2 ((n - i)/(n b0) + i/(
n b1))^2))^(1/(n + 1)), {i, 0, n}]
The m0,m1,b0,b1,x are real and b0>0,b1>0
All four combinations of assumptions in the form of m1>m0,b1>b0 were tested, however the expression was returned unevaluated.
A FullSimplify of prd is running at the moment for 6 hours unterminated on a computer with sufficient ram (8 gb).
Any ideas would be highly appreciated.
Igor Igel
URL: , |
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