2
$\begingroup$

Let $ L_{d}^{(1)}(x)$ denote the generalized Laguerre polynomial of degree $d$ and order $\alpha=1$. Clearly, since all the roots $r_1,\dots,r_d$ of $L_{d}^{(1)}$ are simple, there exists a strictly positive function $C=C(d)$ for which $$ \min_{i=1,\dots,d} |L'^{(1)}_{d} (r_i)| \geq C(d) > 0.$$

I would like to have a lower asymptotic bound for $C(d)$ (i.e. as rapidly increasing/slowly decreasing as possible).

$\endgroup$

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.