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We show that the each member of the confluent family of the Gausshypergeometric equations is realized as quantum curves for appropriate spectralcurves. As an application, relations between the Voros coefficients of thoseequations and the free energy of their classical limit computed by thetopological recursion are established. We will also find explicit expressionsof the free energy and the Voros coefficients in terms of the Bernoulli numbersand Bernoulli polynomials.

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