Chebyshev polynomials on circular arcs
In this paper, we give anexplicit representation of the complex Chebyshev polynomials on a given arc of the unit circle (in the complex plane)in terms of real Chebyshev polynomials on two symmetric intervals (on thereal line). The real Chebyshev polynomials, for their part, can be expressedvia a con...
Elmentve itt :
| Dokumentumtípus: | Cikk |
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| Megjelent: |
2019
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| Sorozat: | Acta scientiarum mathematicarum
85 No. 3-4 |
| Kulcsszavak: | Csebisev-polinomok, Körív, Jacobi elliptikus függvény, Jacobi théta függvény |
| doi: | 10.14232/actasm-018-343-y |
| Online Access: | http://acta.bibl.u-szeged.hu/66337 |
| Tartalmi kivonat: | In this paper, we give anexplicit representation of the complex Chebyshev polynomials on a given arc of the unit circle (in the complex plane)in terms of real Chebyshev polynomials on two symmetric intervals (on thereal line). The real Chebyshev polynomials, for their part, can be expressedvia a conformal mapping with the help of Jacobian elliptic and theta functions,which goes back to the work of Akhiezer in the 1930’s |
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| Terjedelem/Fizikai jellemzők: | 629-649 |
| ISSN: | 2064-8316 |