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Watson's basic analogue of Ramanujan's entry 40 and its generalization

Dharma P. Gupta·David R. Masson
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Abstract

We generalize Watson's $ q $-analogue of Ramanujan's Entry 40 continued fraction by deriving solutions to a $ {}_{10} ϕ_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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Dharma P. Gupta, David R. Masson. 1993-12-29. Watson's basic analogue of Ramanujan's entry 40 and its generalization. https://arxiv.org/abs/math/9312211

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