Research of hypergeometric functions with multi-variables via computer algebra
Project/Area Number |
22540179
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Single-year Grants |
Section | 一般 |
Research Field |
Basic analysis
|
Research Institution | Kanazawa University |
Principal Investigator |
|
Project Period (FY) |
2010 – 2012
|
Project Status |
Completed (Fiscal Year 2012)
|
Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
Keywords | 複素解析 / 超幾何関数 / 数式処理 / ホロノミック系 / 微分差分方程式 / グレブナー基底 / 計算数学 / 代数統計 / 微分作用素環 |
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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Report
(4 results)
Research Products
(23 results)