The hypergeometric function, the confluent hypergeometric function and WKB solutions

DOI10.2969/jmsj/84528452zbMath1496.33002OpenAlexW3192609840MaRDI QIDQ2058812

Takashi Aoki, Mika Tanda, Toshinori Takahashi

Publication date: 10 December 2021

Published in: Journal of the Mathematical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/journals/journal-of-the-mathematical-society-of-japan/volume-73/issue-4/The-hypergeometric-function-the-confluent-hypergeometric-function-and-WKB-solutions/10.2969/jmsj/84528452.full

zbMATH Keywords

asymptotic expansionhypergeometric differential equationVoros coefficientWKB solutionconfluent hypergeometric differential equation

Mathematics Subject Classification ID

Classical hypergeometric functions, ({}_2F_1) (33C05) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Stokes phenomena and connection problems (linear and nonlinear) for ordinary differential equations in the complex domain (34M40)

Related Items (2)

Degeneration structure of the Voros coefficients of the generalized hypergeometric differential equations with a large parameter ⋮ Voros coefficients at the origin and at the infinity of the generalized hypergeometric differential equations with a large parameter

Cites Work

• Parametric Stokes phenomena of the Gauss hypergeometric differential equation with a large parameter
• On the Voros coefficient for the Whittaker equation with a large parameter -- some progress around Sato's conjecture in exact WKB analysis
• Large parameter cases of the Gauss hypergeometric function
• Uniform asymptotic expansions for hypergeometric functions with large parameters IV
• Asymptotics of the Gauss hypergeometric function with large parameters, I
• Asymptotics of the Gauss hypergeometric function with large parameters, II
• The relation between the Bessel function and the Borel sum of the WKB solution
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS III
• Uniform Asymptotic Expansions of Confluent Hypergeometric Functions
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS I
• UNIFORM ASYMPTOTIC EXPANSIONS FOR HYPERGEOMETRIC FUNCTIONS WITH LARGE PARAMETERS II
• WKB Analysis and Stokes Geometry of Differential Equations
• Voros coefficients of the Gauss hypergeometric differential equation with a large parameter
• Voros coefficients for the hypergeometric differential equations and Eynard–Orantin’s topological recursion: Part II: For confluent family of hypergeometric equations
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