Ramanujan's {_1\psi_1} summation
Combinatorics
2013-04-08 v3 Number Theory
Quantum Algebra
Abstract
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.
Cite
@article{arxiv.1206.2435,
title = {Ramanujan's {_1\psi_1} summation},
author = {S. Ole Warnaar},
journal= {arXiv preprint arXiv:1206.2435},
year = {2013}
}
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