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Searching for an asymptotic to exp[0.5]
#52
NOTE :

For those who want to conjecture the inverse of conjecture T1 ;

If f_3(z) is stable , then so is f_1(z).

THIS IS FALSE !

For instance if f_2(z) = eps + z^2.

Notice

1 + z + z^2/sqrt(2) + z^3/sqrt(6) + z^4/sqrt(24) = 0
has the zero :
0.2026 + 1.5304 i
and
1 + z + z^2/sqrt(2) + z^3/sqrt(6) + z^4/sqrt(24) + z^5/sqrt(120) = 0
has the zero :
0.545368 + 1.61261 i

Hence disproving the inverse of conjecture T1.

Btw taking more terms to avoid polynomials : g(z) = 1 + z + z^2/sqrt(2) + z^3/sqrt(6) + z^4/sqrt(24) + z^5/sqrt(120) + ... only makes the case more Obvious.
g(z) has zero's with an unbounded large real part.

( or so it appears , anyway the trends seems growing , unbounded is a " mini conjecture / exercise " for those who are intrested ).

regards

tommy1729
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Messages In This Thread
RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 07/15/2014, 09:43 PM

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