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  1. Theoretical and Mathematical Physics
  2. Theoretical and Mathematical Physics : Volume 119
  3. Theoretical and Mathematical Physics : Volume 119, Issue 1, April 1999
  4. Structural theory of special functions
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Theoretical and Mathematical Physics : Volume 191
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Theoretical and Mathematical Physics : Volume 121
Theoretical and Mathematical Physics : Volume 120
Theoretical and Mathematical Physics : Volume 119
Theoretical and Mathematical Physics : Volume 119, Issue 3, June 1999
Theoretical and Mathematical Physics : Volume 119, Issue 2, May 1999
Theoretical and Mathematical Physics : Volume 119, Issue 1, April 1999
Structural theory of special functions
An Ablowitz-Ladik system with a discrete potential: I. Extended resolvent
Equations of motion and conserved quantities in non-Abelian discrete integrable models
Miura-type transformations of nonlinear partial differential equations integrable by the $$\bar \partial$$ -problem methodmethod
Renormalization group, causality, and nonpower perturbation expansion in QFT
Wigner function for free relativistic particles
H-model of critical dynamics: Two-loop calculations of RG functions and critical indices
On the quasi-classical limit of the quadratic susceptibility
A (2+1)-dimensional fermion in the Coulomb and magnetic field backgrounds
Exact solutions of classical electrodynamics and the Yang-Mills-Wong theory in even-dimensional space-time
Fermi-Walker transport and the Weyl connection
Two-time temperature Green’s functions in kinetic theory and molecular hydrodynamics: II. Equations for pair-interaction systems
Classical statistics of one-component systems with model potentials
Theoretical and Mathematical Physics : Volume 118
Theoretical and Mathematical Physics : Volume 117
Theoretical and Mathematical Physics : Volume 116
Theoretical and Mathematical Physics : Volume 115
Theoretical and Mathematical Physics : Volume 114
Theoretical and Mathematical Physics : Volume 113
Theoretical and Mathematical Physics : Volume 112
Theoretical and Mathematical Physics : Volume 111
Theoretical and Mathematical Physics : Volume 110

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Structural theory of special functions

Content Provider Springer Nature Link
Author Slavyav, S. Yu.
Copyright Year 1999
Abstract A block diagram is suggested for classifying differential equations whose solutions are special functions of mathematical physics. Three classes of these equations are identified: the hypergeometric, Heun, and Painlevé classes. The constituent types of equations are listed for each class. The confluence processes that transform one type into another are described. The interrelations between the equations belonging to different classes are indicated. For example, the Painlevé-class equations are equations of classical motion for Hamiltonians corresponding to Heun-class equations, and linearizing the Painlevé-class equations leads to hypergeometric-class equations. The “confluence principle” is stated, and an example of its application is given.
Starting Page 393
Ending Page 406
Page Count 14
File Format PDF
ISSN 00405779
Journal Theoretical and Mathematical Physics
Volume Number 119
Issue Number 1
e-ISSN 15739333
Language English
Publisher Kluwer Academic Publishers-Plenum Publishers
Publisher Date 1999-01-01
Publisher Place New York
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Applications of Mathematics Mathematical and Computational Physics
Content Type Text
Resource Type Article
Subject Statistical and Nonlinear Physics Mathematical Physics
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