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DOI :10.26650/ijmath.2024.00011   IUP :10.26650/ijmath.2024.00011    Tam Metin (PDF)

On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument

Hironobu Kimura

We investigate the several special functions defined by a matrix integral on the Hermitian matrix space of size n. They are the matrix argument analogues of the Gauss hypergeometric, Kummer’s confluent hypergeometric, the Bessel, the Hermite-Weber and Airy functions which play important roles in the multivariate statistical analysis and the random matrix theory. We give the integral representations for them as functions of eigenvalues of the matrix argument by using the result of Harish-Chandra and Itzykson-Zuber, and give the systems of differential equations for them. We show that these system are holonomic and have the holonomic rank 2 𝑛 using the theory of Gröbner basis.

Anahtar Kelimeler: hypergeometric function, matrix integral, holonomic system, Gröbner basis

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Referanslar

  • M. Adler and P. van Moerbeke, 1992, A matrix integral solution to two-dimensional Wp-gravity. Commun. Math. Phys. 147, 25-56. google scholar
  • A.B. Balantekin, 2000, Character expansions, Itzykson-Zuber integrals, and the QCD partition function. Phys. Rev. D (3) 62, no. 8, 085017. google scholar
  • P. M. Bleher and A. B. J. Kuijlaars, 2004, Random matrices with external source and multiple orthogonal polynomials. Int. Math. Res. Not., no. 3, 109-129. google scholar
  • P. Deift, 2000, Orthogonal Polynomials and Random Matrices: A Riemann-Hilbert Approach, Courant Lecture Notes in Mathematics 3, Amer. Math. Soc., Providence RI. google scholar
  • J. Faraut and A. Koranyi. 1994, Analysis on symmetric cones, Oxford Math. monographs. google scholar
  • J. Harnad and A. Yu. Orlov, 2007, Fermionic construction of tau functions and random processes. Phys. D 235 no. 1-2, 168-206. google scholar
  • M. Hien, 2007, Periods for irregular singular connections on surface, Math. Ann. 337, 631-669. google scholar
  • K. Iwasaki, H. Kimura, S. Shimomura and M. Yoshida, 1991, From Gauss to Painleve. Vieweg Verlag. google scholar
  • K. Inamasu and H. Kimura, 2021, Matrix hypergeometric functions, semi-classical orthogonal polynomials and quantum Painleeequations. Integral Transforms Spec. Funct. 32, no. 5-8, 528-544. google scholar
  • H. Kimura and T. Koitabashi, 1996, Normalizer of maximal abelian subgroup of GL(n)and general hypergeometric functions. Kumamoto J. Math. 9, 13-43. google scholar
  • M. Kontsevich, 1992, Intersection theory on the moduli space of curves and the matrix Airy function. Comm. Math. Phys. 147, no. 1, 1-23. google scholar
  • M.L. Mehta, 1991, Random matrices. Second edition, Academic Press, Boston, MA. google scholar
  • R. J. Muirhead, 1970, Systems of partial differential equations for hypergeometric functions of matrix arguments. Ann. Math. Statistics 41, 991-1001. google scholar
  • R. J. Muirhead, 1982, Aspects of Multivariate Statistical Theory, John Wiley & Sons. google scholar
  • H. Nagoya, 2011, Hypergeometric Solutions to Schrödinger equations for the quantum Painleve equations. J. Math. Phys. 52, no. 8, 083509. google scholar

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APA

Kimura, H. (2024). On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument. Istanbul Journal of Mathematics, 2(1), 1-27. https://doi.org/10.26650/ijmath.2024.00011


AMA

Kimura H. On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument. Istanbul Journal of Mathematics. 2024;2(1):1-27. https://doi.org/10.26650/ijmath.2024.00011


ABNT

Kimura, H. On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument. Istanbul Journal of Mathematics, [Publisher Location], v. 2, n. 1, p. 1-27, 2024.


Chicago: Author-Date Style

Kimura, Hironobu,. 2024. “On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument.” Istanbul Journal of Mathematics 2, no. 1: 1-27. https://doi.org/10.26650/ijmath.2024.00011


Chicago: Humanities Style

Kimura, Hironobu,. “On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument.” Istanbul Journal of Mathematics 2, no. 1 (Dec. 2024): 1-27. https://doi.org/10.26650/ijmath.2024.00011


Harvard: Australian Style

Kimura, H 2024, 'On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument', Istanbul Journal of Mathematics, vol. 2, no. 1, pp. 1-27, viewed 10 Dec. 2024, https://doi.org/10.26650/ijmath.2024.00011


Harvard: Author-Date Style

Kimura, H. (2024) ‘On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument’, Istanbul Journal of Mathematics, 2(1), pp. 1-27. https://doi.org/10.26650/ijmath.2024.00011 (10 Dec. 2024).


MLA

Kimura, Hironobu,. “On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument.” Istanbul Journal of Mathematics, vol. 2, no. 1, 2024, pp. 1-27. [Database Container], https://doi.org/10.26650/ijmath.2024.00011


Vancouver

Kimura H. On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument. Istanbul Journal of Mathematics [Internet]. 10 Dec. 2024 [cited 10 Dec. 2024];2(1):1-27. Available from: https://doi.org/10.26650/ijmath.2024.00011 doi: 10.26650/ijmath.2024.00011


ISNAD

Kimura, Hironobu. “On the holonomic systems for the Gauss hypergeometric function and its confluent family of a matrix argument”. Istanbul Journal of Mathematics 2/1 (Dec. 2024): 1-27. https://doi.org/10.26650/ijmath.2024.00011



ZAMAN ÇİZELGESİ


Gönderim08.04.2024
Kabul07.06.2024
Çevrimiçi Yayınlanma25.06.2024

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