| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2022: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
I analyze hypergeometric equations which characterize hypergeometric functions as special functions by applying several transformations including middle convolutions. I define versal unfoldings of ordinary differential equations with unramified irregular singular points and give versal integral representations of their solutions and a transformation theorem of Stokes coefficients of them. If the equations are rigid, I prove that they are versally extended to hypergeometric systems with several variables regarding singular points as variables.
Introducing new integral transformations, I analyze a wide class of hypergeometric systems with many variables which are not necessarily rigid and give integral representations of their solutions, power series expressions of them and their connection formulas etc.
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