ON PARTICULAR SOLUTIONS OF THE GARNIER SYSTEMS AND THE HYPERGEOMETRIC FUNCTIONS OF SEVERAL VARIABLES

DOI10.1093/qmath/37.1.61zbMath0597.35114OpenAlexW1984433083MaRDI QIDQ3729484

Hironobu Kimura, Kazuo Okamoto

Publication date: 1986

Published in: The Quarterly Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1093/qmath/37.1.61

zbMATH Keywords

Hamiltonian systemPainlevé equationsLauricella's hypergeometric functiongeneralization of the Bessel functionN-dimensional Garnier system

Mathematics Subject Classification ID

Partial differential equations of mathematical physics and other areas of application (35Q99) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Hypergeometric integrals and functions defined by them ((E), (G), (H) and (I) functions) (33C60)

Related Items (20)

The generalized confluent hypergeometric functions ⋮ Toda equation and special polynomials associated with the Garnier system ⋮ On an Airy function of two variables. ⋮ Hypergeometric solution of \(q\)-Schlesinger system of rank two ⋮ Topological recursion and uncoupled BPS structures. II: Voros symbols and the \(\tau\)-function ⋮ On an Airy function of two variables. II ⋮ Voros coefficients and the topological recursion for the hypergeometric differential equation of type (1, 4) ⋮ Canonical structure and symmetries of the Schlesinger equations ⋮ ON THE VARIANCE OF THE INDEX FOR THE GAUSSIAN UNITARY ENSEMBLE ⋮ On confluences of general hypergeometric systems ⋮ Ramified covers and tame isomonodromic solutions on curves ⋮ The degeneration of the two dimensional Garnier system and the polynomial Hamiltonian structure ⋮ On a generalized Bessel function of two variables. II: Case of coalescing saddle points ⋮ Unnamed Item ⋮ Triangular Schlesinger systems and superelliptic curves ⋮ Topological recursion and uncoupled BPS structures. I: BPS spectrum and free energies ⋮ Symmetries of the Garnier system and of the associated polynomial Hamiltonian system ⋮ Unnamed Item ⋮ On confluences of the general hypergeometric systems ⋮ Contiguity relations of generalized confluent hypergeometric functions

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