On the tau function of the hypergeometric equation

@article{Bertola2022OnTT,
  title={On the tau function of the hypergeometric equation},
  author={Marco Bertola and Dmitry Korotkin},
  journal={Physica D: Nonlinear Phenomena},
  year={2022}
}

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References

SHOWING 1-10 OF 31 REFERENCES

Monodromy dependence and connection formulae for isomonodromic tau functions

We discuss an extension of the Jimbo–Miwa–Ueno differential 1-form to a form closed on the full space of extended monodromy data of systems of linear ordinary differential equations with rational

Tau-Functions and Monodromy Symplectomorphisms

We derive a new Hamiltonian formulation of Schlesinger equations in terms of the dynamical r-matrix structure. The corresponding symplectic form is shown to be the pullback, under the monodromy map,

Connection Problem for the Tau-Function of the Sine-Gordon Reduction of Painlevé-III Equation via the Riemann-Hilbert Approach

We evaluate explicitly, in terms of the Cauchy data, the constant pre-factor in the large $x$ asymptotics of the Painleve III tau-function. Our result proves the conjectural formula for this

Fredholm Determinant and Nekrasov Sum Representations of Isomonodromic Tau Functions

We derive Fredholm determinant representation for isomonodromic tau functions of Fuchsian systems with n regular singular points on the Riemann sphere and generic monodromy in GL

Isomonodromic Tau-Functions from Liouville Conformal Blocks

The goal of this note is to show that the Riemann–Hilbert problem to find multivalued analytic functions with $${{\rm SL}(2,\mathbb{C})}$$SL(2,C)-valued monodromy on Riemann surfaces of genus zero

Two and three point functions in Liouville theory