Voros Coefficients for the Hypergeometric Differential Equations and Eynard-Orantin's Topological Recursion - Part II : For the Confluent Family of Hypergeometric Equations

2018/10/06 by Kohei Iwaki, Iwaki, Kohei, Tatsuya Koike +3 · 1 citation
Physics and Astronomy · Computer Science · Mathematics · #Nonlinear Waves and Solitons #Polynomial and algebraic computation #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1810.02946

Abstract

We show that the each member of the confluent family of the Gauss hypergeometric equations is realized as quantum curves for appropriate spectral curves. As an application, relations between the Voros coefficients of those equations and the free energy of their classical limit computed by the topological recursion are established. We will also find explicit expressions of the free energy and the Voros coefficients in terms of the Bernoulli numbers and Bernoulli polynomials.

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• Topological recursion and uncoupled BPS structures I: BPS spectrum and free energies

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