Research of hypergeometric differential-difference equations

• Project/Area Number: 19740069
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Basic analysis
• Research Institution: Kanazawa University
• Principal Investigator: OHARA Katsuyoshi Kanazawa University, 数物科学系, 助教 (00313635)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥2,200,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥300,000); Fiscal Year 2009: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: 複素解析 / 超幾何関数 / 微分差分方程式 / 計算数学 / 変換公式

Research Abstract

In this research, we proved theorems for hypergeometric functions by using hypergeometric differential-difference equations. We studied the rank theory for A-hypergeometric differential-difference equations. We found new transformation formulas for Lauricella's hypergeometric functions of 2 and 3 variables. We developed mathematical software on computer algebra system.

Research Products

• [Journal Article] Holonomic rank of A-hypergeometric differential-difference equations (2009)
  • Author(s): Ohara, K., Takayama, N.
  • Journal Title: Journal of Pure and Applied Algebra 213-8 Pages: 1536-1544
  • NAID: 120001506673
  • Peer Reviewed
• [Journal Article] Some transformation formulas for Lauricella's hypergeometric functions FD (2009)
  • Author(s): Matsumoto, K., Ohara, K.
  • Journal Title: Funkcialaj Ekvacioj 52-2 Pages: 203-212
  • NAID: 130000140519
  • Peer Reviewed
• [Journal Article] Spectral Decomposition and Eigenvectors of Matrices by Residue Calculus (2009)
  • Author(s): Ohara, K., Tajima, S.
  • Journal Title: Proceedings of the Joint Conference of ASCM 2009 and MACIS 2009, COE Lecture Note 22 Pages: 137-140
  • Peer Reviewed
• [Journal Article] Spectral Decomposition and Eigenvectors of Matrices by Residue Calculus (2009)
  • Author(s): K.Ohara, S.Tajima
  • Journal Title: Proceedings of the Joint Conference of ASCM 2009 and MACIS 2009, COE Lecture Note, Kyushu University 22 Pages: 137-140
  • Peer Reviewed
• [Journal Article] Some transformation formulas for Lauricella's hypergeometric functions F_D (2009)
  • Author(s): K. Matsumoto, K. Ohara
  • Journal Title: Funkcialaj Ekvacioj (掲載確定)
  • Peer Reviewed
• [Journal Article] Holonomic rank of A-hypergeometric differential-difference equations (2008)
  • Author(s): K. Ohara, N. Takayama
  • Journal Title: Journal of Pure and Applied Algebra
  • NAID: 120001506673
  • Peer Reviewed
• [Presentation] Spectral Decomposition and Eigenvectors of Matrices by Residue Calculus (2009)
  • Author(s): Ohara, K., Tajima, S.
  • Organizer: The Joint Conference of ASCM 2009 and MACIS 2009
  • Place of Presentation: JALリゾートシーホークホテル福岡(福岡県)
  • Year and Date: 2009-12-14
• [Remarks]
  • URL: http://air.s.kanazawa-u.ac.jp/~ohara/
• [Remarks]
  • URL: http://air.s.kanazawa-u.ac.jp/~ohara/index-j.html
• [Remarks]
  • URL: http://air.s.kanazbwa-u.ac.jp/~ohara/index-j.html
• [Remarks]
  • URL: http://air.s.kanazawa-u.ac.jp/~ohara/index-j.html