Summation and transformation formulas for elliptic hypergeometric series

By S. Ole Warnaar. 2000

160 citations recorded by the source corpus.

Using matrix inversion and determinant evaluation techniques we prove several summation and transformation formulas for terminating, balanced, very-well-poised, elliptic hypergeometric series.

Subfields: Algebra and Number Theory, Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/fc647015e68815b32df82220cb44424e09f721b1

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In Algebra and Number Theory

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Transformations of elliptic hypergeometric integrals (2010, background): “(This is, for instance, a special case of a determinant identity of Warnaar [37], and can also be obtained as a special case of the Cauchy determinant.”
Essays on the theory of elliptic hypergeometric functions (2008, methodology): “I am deeply indebted to my coauthors J. F. van Diejen, E. M. Rains, S. O. Warnaar and A. S. Zhedanov for a fruitful collaboration and many stimulating discussions.”
Extensions of the well-poised and elliptic well-poised Bailey lemma (2003, background): “For a more extensive introduction to elliptic hypergeometric series we refer the reader to [6, 7, 8, 9, 10, 12, 14, 15, 16, 18, 19, 20, 21, 23].”
Inversions of integral operators and elliptic beta integrals on root systems (2004, unknown): “For n an integer the elliptic shifted factorial is defined by [28] (a; q, p)n = Γ(aq; p, q) Γ(a; p, q) (this was denoted as θ(a; p; q)n in [6, 7, 24]).”
$BC_n$-symmetric abelian functions (2004, background): “1 of [29]), via the case t = q, b = q−k, κ = 0 above, in the following way.”
An Elliptic Macdonald-Morris Conjecture and Multiple Modular Hypergeometric Sums (2000, methodology): “Theorems 3 and 5 (together with Frenkel-Turaev’s proof for n = 1 [FT] and computer experiments for n > 1 mentioned in [Wa]) provide additional evidence that Warnaar’s multidimensional modular hypergeometric summation conjecture (6.”
Elliptic hypergeometric series on root systems (2002, methodology): “ive approach should add something to our understanding also of the rational and trigonometric levels. The present paper is not the ﬁrst to deal with elliptic hypergeometric series on root systems. In [W], Warnaar proved one multivariable elliptic analogue of Jackson’s 8W7 summation formula (cf. (7.1”
Positivity preserving transformations for $q$-binomial coefficients (2003, unknown): “There is of course ample precedent for base-changing transformations; see, e.g., [1, 13, 20, 28, 29, 30, 52, 53, 56 ].”
Transformations of elliptic hypergometric integrals (2003, background): “(3.18) (This is, for instance, a special case of a determinant identity of Warnaar [36], and can also be obtained as a special case of the Cauchy determinant.)”