2012 Fiscal Year Final Research Report
Research of hypergeometric functions with multi-variables via computer algebra
| Project/Area Number |
22540179
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Keywords | 複素解析 / 超幾何関数 / 数式処理 |
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| Research Abstract |
In this research, we introduced formulas for some hypergeometric functions with multi-variables using by computer algebra. We found the Pfaffian differential system for the Fisher-Bingham integral and the Fisher integral. In order to apply formulas to Maximum Likelihood Estimation on statistics, we developed new symbolic-numerical method “Holonomic Gradient Descent” and solved concrete MLE problems. Moreover we implemented mathematical software.
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