Special functions emerging from symmetries of the space of solutions to special double confluent Heun equation

DOI10.1007/S40879-022-00583-ZOpenAlexW4302307013MaRDI QIDQ2095624

S. I. Tertychnyi

Publication date: 17 November 2022

Published in: European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.12377

zbMATH Keywords

special functionslinear ordinary differential equationsdouble confluent Heun equationcomplex domainsymmetries of the space of solutions

Mathematics Subject Classification ID

Explicit solutions, first integrals of ordinary differential equations (34A05) Group actions and symmetry properties (58D19) Other functions coming from differential, difference and integral equations (33E30) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Ordinary differential equations on complex manifolds (34M45) Linear ordinary differential equations and systems in the complex domain (34M03)

Cites Work

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• Antiquantization of deformed Heun-class equations
• Automorphisms of the solution spaces of special double-confluent Heun equations
• Geometry of the Prytz planimeter
• Heun functions and some of their applications in physics
• From Heun class equations to Painlevé equations
• Solution space monodromy of a special double confluent Heun equation and its applications
• Holomorphic solutions of the double confluent Heun equation associated with the RSJ model of the Josephson junction
• Tractrices, Bicycle Tire Tracks, Hatchet Planimeters, and a 100-year-old Conjecture
• Tire Tracks and Integrable Curve Evolution

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