2011 Fiscal Year Final Research Report
Identities between Special Functions
| Project/Area Number |
20740075
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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 |
Basic analysis
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| Research Institution | Kobe University |
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Principal Investigator |
VIDUNAS Raimundas 神戸大学, 自然科学系先端科学融合研究環重点研究部, 助教 (00467680)
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| Project Period (FY) |
2008 – 2011
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| Keywords | 超幾何関数 / Appell関数 / Heun関数 / Painleve方程式 / Belyi map |
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| Research Abstract |
I classified univariate specializations of Appell's functions to Gauss hypergeometric functions. One particular case relates explicitly dihedral Gauss hypergeometric functions to terminating rectangular Appell's hypergeometric sums. Similarly, the quadratic invariant for the dihedral hypergeometric functions was expressed as a terminating double hypergeometric sum by generalizing Clausen's identity. Together with Filipuk and van Hoiej, I classified pull-back transformations between Heun and Gauss hypergeometric functions. In total, 61 parametric transformations and 366 transformations in the hyperbolic case were found. Finally, I worked with Marta Mazzocco on transformations of Painleve VI equations and their isomonodromic systems.
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