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Generalizations of Ramanujan's reciprocity formula and the Askey-Wilson integral (1306.2596v1)
Published 14 May 2013 in math.CA
Abstract: By using two known transformation formulas for basic hypergeometric series, we establish a direct extension of Bailey's $_6\psi_6$-series identity. Subsequently, it and Milne's identity are employed to drive multi-variable generalizations of Ramanujan's reciprocity formula. Then we utilize also Milne's identity to deduce a multi-variable generalization of the Askey-Wilson integral.
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