TL;DR
This paper reviews Ramanujan's {_1racepsi_1} summation, exploring its history, applications, and various generalisations including non-commutative and affine root system extensions.
Contribution
It provides a comprehensive overview of Ramanujan's {_1racepsi_1} summation and its extensions, highlighting new generalisations and applications.
Findings
Historical overview of Ramanujan's {_1racepsi_1} summation
Applications to sums of squares and orthogonal polynomials
Extensions to non-commutative and affine root systems
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.
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Taxonomy
TopicsAdvanced Mathematical Identities · Analytic Number Theory Research · Mathematical Inequalities and Applications