2013 Fiscal Year Final Research Report
Integrable system and middle convolution
| Project/Area Number |
22740107
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Global analysis
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| Research Institution | Chuo University |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 可積分系 / 数理物理 / 複素領域の微分方程式 / ホインの微分方程式 / パンルヴェ方程式 / ミドルコンボルーション |
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| Research Abstract |
We investigated Heun's differential equation in the case that one of the sigularity is apparent. By applying middle convolution for it, we obtain an equation which admits a polynomial-type solution, and we have integral representations of solutions of the original differential equation. We also studied it with a connenction to generalized hypergeometric equations.
We obtained results on multi-indexed orthogonal polynomials and on ultradiscrete Painleve equations.
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