Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Applications of $ q$-Lagrange inversion to basic hypergeometric series

Authors: Ira Gessel and Dennis Stanton
Journal: Trans. Amer. Math. Soc. 277 (1983), 173-201
MSC: Primary 33A35; Secondary 05A19, 10A45
MathSciNet review: 690047
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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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Keywords: Lagrange inversion, basic hypergeometric series, Rogers-Ramanujan identities
Article copyright: © Copyright 1983 American Mathematical Society