@ means approximation.
Lemma
\( Exp_a^[b] (x) @ Exp^[b] ( @ Ln(a) x) \)
From there we get
\( Exp_q^{[1/2]}(x) Exp_s^{[1/2]}(x) @ Exp_d^{[1/2]}(x) \)
Where d is
\( Exp(d) = @ Ln^{[1/2]}( Exp^{[1/2]}( Ln(q) x) Exp^{[1/2]} ( Ln(s) x) ) / x \)
( notice this can be rewritten with 1 semi-exp and 2 semi-logs too )
But this is not the full story ofcourse.
We need proofs.
Perhaps consider other ways to handle the issue.
And a qualitative understanding of the formula for d such as d ~ (qs)^2 or the alike.
I wonder if you would have done it differently ?
Also a table would be nice.
Still alot of work to do.
Regards
Tommy1729
The master
Lemma
\( Exp_a^[b] (x) @ Exp^[b] ( @ Ln(a) x) \)
From there we get
\( Exp_q^{[1/2]}(x) Exp_s^{[1/2]}(x) @ Exp_d^{[1/2]}(x) \)
Where d is
\( Exp(d) = @ Ln^{[1/2]}( Exp^{[1/2]}( Ln(q) x) Exp^{[1/2]} ( Ln(s) x) ) / x \)
( notice this can be rewritten with 1 semi-exp and 2 semi-logs too )
But this is not the full story ofcourse.
We need proofs.
Perhaps consider other ways to handle the issue.
And a qualitative understanding of the formula for d such as d ~ (qs)^2 or the alike.
I wonder if you would have done it differently ?
Also a table would be nice.
Still alot of work to do.
Regards
Tommy1729
The master