[VA] SRC#001 - Spiky Integral

[Albert Chan]

(07-21-2018 04:06 AM)Gerson W. Barbosa Wrote:  Thanks both for the I(20000) result and for another interesting approach. These results might be useful to improve the correction terms of the approximation formula.

Hi Gerson,

I am a bit late to the game, and just realized your number is also an approximation.
So, both numbers matching are nice, but probably not good enough.

Instead, I tried I(1000) ~ 4 \(\int_{0}^{\pi /2000} F dx \) = 0.00027425815360837926

From Valentin Albillo last post, my estimate match correct values, to 15 digits
Comparing values in binary form, accuracy is even better, mine is just 6 ULP over !

Thanks Valentin.

I am amazed at how your integration function work.
You mentioned the problems of it computing I(20000).
Shrinking the integral range 800,000 times may help: (0 to Pi/400000) instead of (0, 2 Pi)