Аннотация:
We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral.
This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this polytope. We can subsequently obtain various relations, such as transformations and three-term relations, of these functions by considering geometrical properties of this polytope. The most general functions we describe in this way are sums of two very-well-poised 10ϕ9's and their Nassrallah–Rahman type integral representation.
Образец цитирования:
Fokko J. van de Bult, Eric M. Rains, “Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions”, SIGMA, 5 (2009), 059, 31 pp.
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\paper Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions
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\papernumber 059
\totalpages 31
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Эта публикация цитируется в следующих 7 статьяx:
Howard S. Cohl, Roberto S. Costas-Santos, “Utility of integral representations for basic hypergeometric functions and orthogonal polynomials”, Ramanujan J, 61:2 (2023), 649
Arreche C.E. Dreyfus T. Roques J., “Differential Transcendence Criteria For Second-Order Linear Difference Equations and Elliptic Hypergeometric Functions”, J. Ecole Polytech.-Math., 8 (2021), 147–168
van de Bult F.J., Rains E.M., “Limits of Elliptic Hypergeometric Biorthogonal Functions”, J. Approx. Theory, 193:SI (2015), 128–163
Ito M., Witte N.S., “on a Family of Integrals That Extend the Askey–Wilson
Integral”, J. Math. Anal. Appl., 421:2 (2015), 1101–1130
Milne, S.C., Newcomb, J.W., “Nonterminating q-whipple transformations for basic hypergeometric series in U(n)”, Developments in Mathematics, 23 (2012), 181–224
Spiridonov V.P., Vartanov G.S., “Elliptic Hypergeometry of Supersymmetric Dualities”, Comm Math Phys, 304:3 (2011), 797–874
van de Bult F.J., “An elliptic hypergeometric integral with W(F (4)) symmetry”, Ramanujan J, 25:1 (2011), 1–20
Цитирование в формате AMSBIB
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