| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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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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