S. Ole Warnaar
Published 2012-06-12, updated 2012-11-05Version 3
This paper gives a short but reasonably comprehensive review of Ramanujan's {_1\psi_1} summation and its generalisations. It covers the history of Ramanujan's summation, simple applications to sums of squares and orthogonal polynomials, non-commutative generalisations, and generalisations to affine root systems.
Comments: This paper is part of a series of short articles on Ramanujan's mathematics to appear in the Notices of the AMS in commemoration of Ramanujan's 125th birthday; Final updated and corrected version as will appear in the Notices
Journal: Notices of the AMS, 60, Number 1 (2013), 18-22
On q-Hermite polynomials and their relationship with some other families of orthogonal polynomials
Orthogonal polynomials and Smith normal form
Some combinatorial interpretations of the Macdonald identities for affine root systems
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