12/12/2021, 10:02 PM
A nice example of what fake function theory can do and seems nontrivial without it is the following result.
* notice sums and their related integrals can be close *
For positive \( x \) sufficiently large we get
\( \int_1^{\infty} \exp(xt-t^3) dt <\frac{2\exp(\frac{2\sqrt3x^{3/2}}{9})}{ln(x)} \)
Comments, sharper bounds or alternative methods are welcome.
regards
tommy1729
Tom Marcel Raes
* notice sums and their related integrals can be close *
For positive \( x \) sufficiently large we get
\( \int_1^{\infty} \exp(xt-t^3) dt <\frac{2\exp(\frac{2\sqrt3x^{3/2}}{9})}{ln(x)} \)
Comments, sharper bounds or alternative methods are welcome.
regards
tommy1729
Tom Marcel Raes
