Titlebook: Analytic, Algebraic and Geometric Aspects of Differential Equations; Będlewo, Poland, Sep Galina Filipuk,Yoshishige Haraoka,Sławomir Michal

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CURT

深陷

Towards the Convergence of Generalized Power Series Solutions of Algebraic ODEsnents) formally satisfying an algebraic (polynomial) ordinary differential equation. This proof is based on the implicit mapping theorem for Banach spaces rather than on the majorant method used in our previous proof. We also discuss some examples of a such type formal solutions of Painlevé equation

yohimbine

On ,-Summability of Formal Solutions for Certain Higher Order Partial Differential Operators with Poth respect to . which have polynomial coefficients in .. We obtain a sufficient condition for the .-summability of formal solutions in terms of a global analyticity and a proper exponential growth estimate of the Cauchy data.

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On Stokes Phenomena for the Alternate Discrete PI Equationnouncement paper we consider Stokes phenomena for (alt-dPI) from the viewpoint of exact WKB analysis. After constructing transseries solutions and defining the Stokes geometry of (alt-dPI), we derive explicit connection formulas that describe Stokes phenomena for transseries solutions of (alt-dPI) o

VEIL

Relation of Semi-Classical Orthogonal Polynomials to General Schlesinger Systems via Twistor Theorylinear system of differential equations on .. There are many works establishing this kind of relations between the Painlevé equations and semi-orthogonal polynomials with the weight functions taking from the integrands for hypergeometric, Kummer, Bessel, Hermite, Airy integrals. Some extension of th

thrombus

outskirts

Reducibility of Hypergeometric Equations the rigid Fuchsian linear ordinary differential equations. If the equations with one variable have more than four singular points, they naturally define hypergeometric equations with several variables including Appell’s hypergeometric equations. We also study the reducibility of such equations with