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Transformations of the Hypergeometric 4 F 3 with One Unit Shift: A Group Theoretic Study

Author

Listed:
  • Dmitrii Karp

    (Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam)

  • Elena Prilepkina

    (School of Economics and Management, Far Eastern Federal University, Vladivostok 690950, Russia
    Institute of Applied Mathematics, Far Eastern Branch of the Russian Academy of Sciences, Vladivostok 690041, Russia)

Abstract

We study the group of transformations of 4 F 3 hypergeometric functions evaluated at unity with one unit shift in parameters. We reveal the general form of this family of transformations and its group property. Next, we use explicitly known transformations to generate a subgroup whose structure is then thoroughly studied. Using some known results for 3 F 2 transformation groups, we show that this subgroup is isomorphic to the direct product of the symmetric group of degree 5 and 5-dimensional integer lattice. We investigate the relation between two-term 4 F 3 transformations from our group and three-term 3 F 2 transformations and present a method for computing the coefficients of the contiguous relations for 3 F 2 functions evaluated at unity. We further furnish a class of summation formulas associated with the elements of our group. In the appendix to this paper, we give a collection of Wolfram Mathematica ® routines facilitating the group calculations.

Suggested Citation

  • Dmitrii Karp & Elena Prilepkina, 2020. "Transformations of the Hypergeometric 4 F 3 with One Unit Shift: A Group Theoretic Study," Mathematics, MDPI, vol. 8(11), pages 1-21, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1966-:d:440574
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    References listed on IDEAS

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    1. Shpot, M.A. & Srivastava, H.M., 2015. "The Clausenian hypergeometric function 3F2 with unit argument and negative integral parameter differences," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 819-827.
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