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Oct 24, 2021 at 14:46 comment added Sergii Voloshyn Yes! This is the case.
Oct 24, 2021 at 14:32 comment added Hjalmar Rosengren So you want to put a bound $\lambda_1\leq N$ on the terms and then look at the asymptotics when $N$ and $N_f$ both tend to $\infty$ with $\kappa=N_f/N$ fixed?
Oct 24, 2021 at 14:19 comment added Sergii Voloshyn Thank you for the answer. However we interesting in another case, if we put condition $\lambda_1<N$ for $\lambda=(\lambda_1,..,\lambda_l)$ we arrive to another expression at the $h=1$ (unlike the - $\kappa^2 \log [1-h^2]$ that diverges in that point), and principally we can make expansion around $h=1$ . First terms appears in another topic mathoverflow.net/questions/406707/… .
Oct 22, 2021 at 7:37 history edited Hjalmar Rosengren CC BY-SA 4.0
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Oct 22, 2021 at 5:03 history answered Hjalmar Rosengren CC BY-SA 4.0