Abstract:
A discrete-time chain, associated with the generalized eigenvalue problem for two Jacobi matrices, is derived. Various discrete and continuous symmetries of this integrable equation are revealed. A class of its rational, elementary and elliptic functions solutions, appearing from a similarity reduction, are constructed. The latter lead to large families of biorthogonal rational functions based upon the very-well-poised balanced hypergeometric series of three types: the standard hypergeometric series 9 F 8, basic series 10ϕ9 and its elliptic analogue 10 E 9. For an important subclass of the elliptic biorthogonal rational functions the weight function and normalization constants are determined explicitly.
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Received: 14 May 1999 / Accepted: 5 September 1999
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Spiridonov, V., Zhedanov, A. Spectral Transformation Chains and Some New Biorthogonal Rational Functions. Comm Math Phys 210, 49–83 (2000). https://doi.org/10.1007/s002200050772
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DOI: https://doi.org/10.1007/s002200050772