Applications of 𝑞-Lagrange inversion to basic hypergeometric series

Gessel, Ira; Stanton, Dennis

doi:10.1090/S0002-9947-1983-0690047-7

Applications of $q$-Lagrange inversion to basic hypergeometric series
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by Ira Gessel and Dennis Stanton

Trans. Amer. Math. Soc. 277 (1983), 173-201

DOI: https://doi.org/10.1090/S0002-9947-1983-0690047-7

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Abstract:

A family of $q$-Lagrange inversion formulas is given. Special cases include quadratic and cubic transformations for basic hypergeometric series. The $q$-analogs of the so-called "strange evaluations" are also corollaries. Some new RogersRamanujan identities are given. A connection between the work of Rogers and Andrews, and $q$-Lagrange inversion is stated.

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