Structural theory of special functions |
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Authors: | S Yu Slavyanov |
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Institution: | (1) St. Petersburg State University, St. Petersburg, Russia |
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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.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 119, No. 1, pp. 3–19, April, 1999. |
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Keywords: | |
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