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Variants of Confluent q-Hypergeometric Equations

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Book cover Geometric and Harmonic Analysis on Homogeneous Spaces and Applications (TJC 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 366))

Abstract

Variants of the q-hypergeometric equation were introduced in our previous paper with Hatano. In this paper, we consider degenerations of the variant of the q-hypergeometric equation, which is a q-analogue of confluence of singularities in the setting of the differential equation. We also consider degenerations of solutions to the q-difference equations.

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References

  1. G. Gasper, M. Rahman, Basic Hypergeometric Series, vol. 96 (Cambridge university press, Cambridge, 2004)

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  2. W. Hahn, On linear geometric difference equations with accessory parameters. Funkcial. Ekvac. 14, 73–78 (1971)

    MathSciNet  MATH  Google Scholar 

  3. N. Hatano, R. Matsunawa, T. Sato, K. Takemura, Variants of \(q\)-hypergeometric equation, to appear in Funkcial. Ekvac.. arXiv:1910.12560

  4. R. Koekoek, P.A. Lesky, R.F. Swarttouw, Hypergeometric Orthogonal Polynomials and Their \(q\)-Analogues. Springer Monographs in Mathematics (Springer, Berlin, 2010)

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  5. Y. Ohyama, A unified approach to \(q\)-special functions of the Laplace type. arXiv:1103.5232

  6. K. Takemura, Degenerations of Ruijsenaars-van Diejen operator and \(q\)-Painleve equations. J. Integr. Syst. 2, xyx008 (2017)

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  7. K. Takemura, On \(q\)-deformations of the Heun equation. SIGMA 14, paper 061 (2018)

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Acknowledgements

The authors are grateful to the referee for valuable comments. The third author would like to thank Professor Yousuke Ohyama for discussions. He was supported by JSPS KAKENHI Grant Number JP18K03378.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo, 112-8551, Japan

    Ryuya Matsunawa & Tomoki Sato

  2. Department of Mathematics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo, 112-8610, Japan

    Kouichi Takemura

Authors
  1. Ryuya Matsunawa
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  2. Tomoki Sato
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  3. Kouichi Takemura
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Corresponding author

Correspondence to Kouichi Takemura .

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Editors and Affiliations

  1. Department of Mathematics, Faculty of Sciences of Sfax, Sfax, Tunisia

    Ali Baklouti

  2. Department of Mathematics, Osaka City University, Osaka, Japan

    Hideyuki Ishi

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Matsunawa, R., Sato, T., Takemura, K. (2021). Variants of Confluent q-Hypergeometric Equations. In: Baklouti, A., Ishi, H. (eds) Geometric and Harmonic Analysis on Homogeneous Spaces and Applications . TJC 2019. Springer Proceedings in Mathematics & Statistics, vol 366. Springer, Cham. https://doi.org/10.1007/978-3-030-78346-4_10

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