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- W2095692732 abstract "Abstract We present a systematic method for proving non-terminating basic hypergeometric identities. Assume that k is the summation index. By setting a parameter x to xq n , we may find a recurrence relation of the summation by using the q -Zeilberger algorithm. This method applies to almost all non-terminating basic hypergeometric summation formulae in the work of Gasper and Rahman. Furthermore, by comparing the recursions and the limit values, we may verify many classical transformation formulae, including the Sears–Carlitz transformation, transformations of the very well-poised 8φ7 series, the Rogers–Fine identity and the limiting case of Watson's formula that implies the Rogers–Ramanujan identities." @default.
- W2095692732 created "2016-06-24" @default.
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- W2095692732 date "2008-10-01" @default.
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- W2095692732 title "Non-Terminating Basic Hypergeometric Series and the <i>q</i>-Zeilberger Algorithm" @default.
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- W2095692732 doi "https://doi.org/10.1017/s0013091506001313" @default.
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