| Autor: |
Deift, Percy, Piorkowski, Mateusz |
| Rok vydání: |
2023 |
| Předmět: |
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| Zdroj: |
SIGMA 20 (2024), 004, 48 pages |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.3842/SIGMA.2024.004 |
| Popis: |
We prove an asymptotic formula for the recurrence coefficients of orthogonal polynomials with orthogonality measure $\log \bigl(\frac{2}{1-x}\bigr) {\rm d}x$ on $(-1,1)$. The asymptotic formula confirms a special case of a conjecture by Magnus and extends earlier results by Conway and one of the authors. The proof relies on the Riemann-Hilbert method. The main difficulty in applying the method to the problem at hand is the lack of an appropriate local parametrix near the logarithmic singularity at $x = +1$. |
| Databáze: |
arXiv |
| Externí odkaz: |
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