Theory and numerical evaluation of special functions of several variables

2016 Fiscal Year Final Research Report

• 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
• Keywords: 超幾何関数 / 数値評価

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.

Free Research Field

特殊関数