09/21/2015, 10:53 AM

I was mostly aware of that Sheldon , in fact that were my thoughts when first reading post 16.

But thank you for sharing your ideas and making those implicit Ideas explicit ( That's how i see it ) and thereby making the thread more complete and readable.

Speaking of post 16 , I have paid alot of attention to post 9 and the correcting factor sqrt(n), but post 16 has a different correcting factor.

But things are subtle.

In TPID 17 I added conditions on the derivatives of the original or best fake.

One of the reasons is partially related to post 16.

In post 16 the fake derivatives depend on f '' alot.

But if f ' ' ' and f ' ' ' ' can be negative and a few other unfortunate properties then the second derivative might not always behave as you want.

Im not going into details here.

However we can combine TPID17 and post 16 and thereby arrive at a Nice conjecture.

When this conjecture is stated in terms of contour integral we get

Conjecture B

I talked about Conjecture B with mick and I advised him to put it on MSE.

More precisely edditing his recent one with adding Conjecture B.

By the time I finish this post it should be there.

So you can read Conjecture B on MSE

http://math.stackexchange.com/questions/...r-dx-n-n-0

---

Am I the only one who wonders what happens if we add the positivity condition f ' ' ' (x) > 0 and then see if we can improve post 16 estimate with a f ' ' ' term !?

Although Sheldon argues that that term has little influence and for exp(x) it has NO influence.

But still.

Regards

Tommy1729

But thank you for sharing your ideas and making those implicit Ideas explicit ( That's how i see it ) and thereby making the thread more complete and readable.

Speaking of post 16 , I have paid alot of attention to post 9 and the correcting factor sqrt(n), but post 16 has a different correcting factor.

But things are subtle.

In TPID 17 I added conditions on the derivatives of the original or best fake.

One of the reasons is partially related to post 16.

In post 16 the fake derivatives depend on f '' alot.

But if f ' ' ' and f ' ' ' ' can be negative and a few other unfortunate properties then the second derivative might not always behave as you want.

Im not going into details here.

However we can combine TPID17 and post 16 and thereby arrive at a Nice conjecture.

When this conjecture is stated in terms of contour integral we get

Conjecture B

I talked about Conjecture B with mick and I advised him to put it on MSE.

More precisely edditing his recent one with adding Conjecture B.

By the time I finish this post it should be there.

So you can read Conjecture B on MSE

http://math.stackexchange.com/questions/...r-dx-n-n-0

---

Am I the only one who wonders what happens if we add the positivity condition f ' ' ' (x) > 0 and then see if we can improve post 16 estimate with a f ' ' ' term !?

Although Sheldon argues that that term has little influence and for exp(x) it has NO influence.

But still.

Regards

Tommy1729