Watson's basic analogue of Ramanujan's entry 40 and its generalization
classification
🧮 math.CA
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watsonanaloguecasecontiguouscontinuedentryfractionramanujan
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We generalize Watson's $ q $-analogue of Ramanujan's Entry 40 continued fraction by deriving solutions to a $ {}_{10} \phi_9 $ series contiguous relation and applying Pincherle's theorem. Watson's result is recovered as a special terminating case, while a limit case yields a new continued fraction associated with an $ \ephis $ series contiguous relation.
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