The q-Borel Sum of Divergent Basic Hypergeometric Series ᵣφₛ(a; b; q, x)
We study the divergent basic hypergeometric series, which is a q-analog of divergent hypergeometric series. This series formally satisfies the linear q-difference equation. In this paper, for that equation, we give an actual solution which admits basic hypergeometric series as a q-Gevrey asymptotic...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2019 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2019
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210059 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The q-Borel Sum of Divergent Basic Hypergeometric Series ᵣφₛ(a; b; q, x) / S. Adachi // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 14 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We study the divergent basic hypergeometric series, which is a q-analog of divergent hypergeometric series. This series formally satisfies the linear q-difference equation. In this paper, for that equation, we give an actual solution which admits basic hypergeometric series as a q-Gevrey asymptotic expansion. Such an actual solution is obtained by using q-Borel summability, which is a q-analog of Borel summability. Our result shows a q-analog of the Stokes phenomenon. Additionally, we show that letting q→1 in our result gives the Borel sum of classical hypergeometric series. The same problem was already considered by Dreyfus, but we note that our result is remarkably different from his.
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| ISSN: | 1815-0659 |