Spectral Transformation Chains and Some New Biorthogonal Rational Functions

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Transformations of elliptic hypergeometric integrals (2010, background): “functions, however; indeed, even in the univariate case, the elliptic analogues of the Askey-Wilson polynomials are merely biorthogonal (these analogues are due to Spiridonov and Zhedanov [33, 34 ] in the discrete case”
Essays on the theory of elliptic hypergeometric functions (2008, methodology): “A generalized (1+1)-dimensional integrable chain similar to the discrete time Toda chain was constructed in the paper [9], and it was shown that the same terminating series with arbitrary parameters appears as a particular solution of the corresponding Lax pair equations.”
An Elliptic Macdonald-Morris Conjecture and Multiple Modular Hypergeometric Sums (2000, methodology): “To simplify the comparison with the results of [FT, SZ ], we rewrite the multiple Frenkel-Turaev summation of Corollary 2 in terms of elliptic numbers, which are defined as”
Transformations of elliptic hypergometric integrals (2003, background): “In the univariate case ([37, 17, 18, 33, 34, 32]), this filtration simply corresponds to a sequence of allowed poles.”
$BC_n$-symmetric abelian functions (2004, background): “In the univariate case, this was proved in Section 9 of [27].”