Another proof of Bailey’s 6ψ6 summation
نویسندگان
چکیده
منابع مشابه
A simple proof of Bailey’s very-well-poised 6ψ6 summation
Using Rogers’ nonterminating 6φ5 summation and elementary series manipulations, we give a simple proof of Bailey’s very-well-poised 6ψ6 summation. This proof extends M. Jackson’s first proof of Ramanujan’s 1ψ1 summation.
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Abstract. By multidimensional matrix inversion, combined with an Ar extension of Jackson’s 8φ7 summation formula by Milne, a new multivariable 8φ7 summation is derived. By a polynomial argument this 8φ7 summation is transformed to another multivariable 8φ7 summation which, by taking a suitable limit, is reduced to a new multivariable extension of the nonterminating 6φ5 summation. The latter is ...
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We present a new proof of Banaschewski's theorem stating that the completion lift of a uniform surjection is a surjection. The new procedure allows to extend the fact (and, similarly, the related theorem on closed uniform sublocales of complete uniform frames) to quasi-uniformities ("not necessarily symmetric uniformities"). Further, we show how a (regular) Cauchy point on a closed uniform subl...
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Adapting a method used by Cauchy, Bailey, Slater, and more recently, the second author, we give a new proof of Bailey’s celebrated 6ψ6 summation formula.
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ژورنال
عنوان ژورنال: Aequationes mathematicae
سال: 2005
ISSN: 0001-9054,1420-8903
DOI: 10.1007/s00010-004-2748-4