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A new multivariable 6 ψ 6 summation formula

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Abstract

By multidimensional matrix inversion, combined with an A r extension of Jackson’s 8 φ 7 summation formula by Milne, a new multivariable 8 φ 7 summation is derived. By a polynomial argument this 8 φ 7 summation is transformed to another multivariable 8 φ 7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6 φ 5 summation. The latter is then extended, by analytic continuation, to a new multivariable extension of Bailey’s very-well-poised 6 ψ 6 summation formula.

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Authors and Affiliations

  1. Fakultät für Mathematik, Universität Wien, Nordbergstraße 15, A-1090, Vienna, Austria

    Michael Schlosser

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  1. Michael Schlosser
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Correspondence to Michael Schlosser.

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Partly supported by FWF Austrian Science Fund grants P17563-N13, and S9607 (the second is part of the Austrian National Research Network “Analytic Combinatorics and Probabilistic Number Theory”).

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Schlosser, M. A new multivariable 6 ψ 6 summation formula. Ramanujan J 17, 305–319 (2008). https://doi.org/10.1007/s11139-007-9017-9

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  • DOI: https://doi.org/10.1007/s11139-007-9017-9

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