On the approximation of certain numbers connected with Jacobi elliptic functions (in Ukrainian) |
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| Author |
Department of Mechanics and Mathematics, Lviv University, Universytetska
1, Lviv, 290602, Ukraine
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| Abstract |
Let $\operatorname{sn} z$, $\omega$ and $\varkappa$ be the notations of the Jacobi elliptic function theory;
let $\beta$ be any complex number different from the poles of $\operatorname{sn} z$. We estimate
from below the simultaneous approximation $\varkappa$, $\omega$, $\beta$ and $\operatorname{sn} \beta$.
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| Keywords |
Jacobi elliptic functions, simultaneous approximation, lower estimate
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| DOI |
doi:10.30970/ms.2.1.10-13
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Reference |
1. Гурвиц А., Курант Р. Теория функций.– М.: Наука, 1968.– 648 с.
2. Фельдман Н.И. Седьмая проблема Гильберта.– М.: Изд-во МГУ, 1982.– 311 с. 3. Reyssat E. Approximation algebrique de nombres lies aux fonctions elliptique et exponentielle // Bull. Soc. Math. France. 1980. N.1. P.47–79. 4. Masser D. Elliptic functions and transcendence // Lect. Notes Math. 1975. V.437. P.1–143 Department of Mechanics and Mathematics, Lviv University, Universytetska 1, Lviv, 290602, Ukraine |
| Pages |
10-13
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| Volume |
2
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| Issue |
1
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| Year |
1993
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| Journal |
Matematychni Studii
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| Full text of paper | |
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