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 Mat. Zametki, 2001, Volume 70, Issue 5, Pages 769–779 (Mi mz788)

General Linear Transformations of Hypergeometric Functions

A. W. Niukkanen

Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences

Abstract: The notion of a canonical form is introduced for multiple hypergeometric series. This notion, in conjunction with the factorization method suggested earlier by the author, is used to obtain the most general explicit descriptions of linear transformations of multiple series that are of Gauss, Kummer, or Bessel type with respect to some variable $x_n$. A complete classification of the 34 Horn series according to their types and forms is given. It is used to show that the transformations described in this paper permit one to obtain the 147 single transformations of Horn series as well as quite a few repeated transformations. A computer program implementing these transformations is developed on the basis of the Maple V-4 computer algebra system.

DOI: https://doi.org/10.4213/mzm788

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English version:
Mathematical Notes, 2001, 70:5, 698–707

Bibliographic databases:

UDC: 517.588+519.68
Revised: 08.07.2001

Citation: A. W. Niukkanen, “General Linear Transformations of Hypergeometric Functions”, Mat. Zametki, 70:5 (2001), 769–779; Math. Notes, 70:5 (2001), 698–707

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz788
• https://doi.org/10.4213/mzm788
• http://mi.mathnet.ru/eng/mz/v70/i5/p769

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. A. V. Niukkanen, “Kvadratichnye preobrazovaniya gipergeometricheskikh ryadov ot mnogikh peremennykh”, Fundament. i prikl. matem., 8:2 (2002), 517–531
2. A. W. Niukkanen, O. S. Paramonova, “Linear Transformations and Reduction Formulas for the Gelfand Hypergeometric Functions Associated with the Grassmannians $G_{2,4}$ and $G_{3,6}$”, Math. Notes, 71:1 (2002), 80–89
3. Niukkanen AW, “On the way to computerizable scientific knowledge (by the example of the operator factorization method)”, Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment, 502:2–3 (2003), 639–642
4. A. W. Niukkanen, “Transformation of the Triple Series of Gelfand, Graev, and Retakh into a Series of the Same Type and Related Problems”, Math. Notes, 89:3 (2011), 374–381
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