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Full Description
This volume contains a collection of papers that focus on recent research in the broad field of special functions. The articles cover topics related to differential equations, dynamic systems, integrable systems, billiards, and random matrix theory. Linear classical special functions, such as hypergeometric functions, Heun functions, and various orthogonal polynomials and nonlinear special functions (e.g., the Painleve transcendents and their generalizations), are studied from different perspectives. This volume serves as a useful reference for a large audience of mathematicians and mathematical physicists interested in modern theory of special functions. It is suitable for both graduate students and specialists in the field.
Contents
Amilcar Branquinho, Ana Foulquie-Moreno, and Manuel Manas, Banded matrices and their orthogonality
M. M. Castro, A. Foulquie-Moreno, and A. Fradi, Time-and-band limiting for matrix-valued orthogonal polynomials related with 2 x 2 hypergeometric operators
Yang Chen and Shulin Lyu, Gaussian unitary ensembles with jump discontinuities, PDEs, and the coupled Painleve IV system
Ewa Ciechanowicz, Properties of meromorphic solutions of certain equations via Nevanlinna theory
Nicholas Ercolani, Joceline Lega, and Brandon Tippings, Map enumeration from a dynamical perspective
Sean Gasiorek and Milena Radnovic, Periodic trajectories and topology of the integrable Boltzmann system
P. R. Gordoa and A. Pickering, Higher-order nonlinear special functions: Painleve hierarchies, a survey
Xing Li and Da-jun Zhang, The Lame functions and elliptic soliton solutions: Bilinear approach
Egmont Porten and Cornelia Schiebold, From the operator KP equation to scalar and matrix-valued solutions
