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Searching for an asymptotic to exp[0.5]
#92
My guess is that fake( exp(x) - (x^3 / 5) ) is simply :
exp(x) - Constant.

But I have not tried anything yet.

I assume the best possible approximation ( by using fake - for exp(x) - ( x^3 / 5 ) - ) is approximately exp(x) - a x^b - constant.
Where b is between 0 and 1.

Also a possibility is with q_i very small :

1 + q_1 x + q_2 x^2 + q_3 x^3 + x^4/4! + x^5/5! + ...

or

0 + q_1 x + q_2 x^2 + q_3 x^3 + x^4/4! + x^5/5! + ...

I wonder.


It seems 0 + q_1 x + q_2 x^2 + q_3 x^3 + x^4/4! + x^5/5! + ...
cannot be improved.
( because O(x^3) cannot be given by O(x^(3+eps)) )

Therefore it would be a good (benchmark) test for our fake algorithms I guess.


regards

tommy1729
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Messages In This Thread
RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/11/2014, 08:02 AM

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