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

Dmitrii Karp and Elena Prilepkina
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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

Mathematics, 2020, vol. 8, issue 11, 1-21

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.

Keywords: generalized hypergeometric function; hypergeometric transformations; transformation groups; symmetric group (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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