Theory and numerical evaluation of special functions of several variables
Project/Area Number |
25287018
|
Research Category |
Grant-in-Aid for Scientific Research (B)
|
Allocation Type | Partial Multi-year Fund |
Section | 一般 |
Research Field |
Basic analysis
|
Research Institution | Kobe University |
Principal Investigator |
Takayama Nobuki 神戸大学, 理学(系)研究科(研究院), 教授 (30188099)
|
Co-Investigator(Kenkyū-buntansha) |
小池 達也 神戸大学, 理学(系)研究科(研究院), 准教授 (80324599)
|
Co-Investigator(Renkei-kenkyūsha) |
HARAOKA Yoshishige 熊本大学, 大学院先端科学研究部(理), 教授 (30208665)
MATSUMOTO Keiji 北海道大学, 理学研究院, 教授 (30229546)
|
Project Period (FY) |
2013-04-01 – 2017-03-31
|
Project Status |
Completed (Fiscal Year 2016)
|
Budget Amount *help |
¥6,630,000 (Direct Cost: ¥5,100,000、Indirect Cost: ¥1,530,000)
Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
|
Keywords | 超幾何関数 / 数値評価 / 多変数超幾何関数 / Borel 総和 / 多変数超幾何多項式 / A超幾何系 / 合流型 A-超幾何関数 / ホロノミック勾配法 / order polytope / Borel変換 |
Outline of Final Research Achievements |
We give an algorithm to evaluate numerically big A-hypergeometric polynomials. An efficient implementation to evaluate numerically the matrix hypergeometric function 1F1 is given. We study divergent series solutions of A-hypergeometric equations and those of Heun type ordinary differential equations in terms of the Borel summability. These theoretical results help to analyze these functions globally and we hope that they give a new method for a numerical analysis of these functions.
|
Report
(5 results)
Research Products
(18 results)