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This article is cited in 5 scientific papers (total in 5 papers)
Structural theory of special functions
S. Yu. Slavyanov Saint-Petersburg State University
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.
Received: 09.07.1998 Revised: 23.11.1998
Citation:
S. Yu. Slavyanov, “Structural theory of special functions”, TMF, 119:1 (1999), 3–19; Theoret. and Math. Phys., 119:1 (1999), 393–406
Linking options:
https://www.mathnet.ru/eng/tmf723https://doi.org/10.4213/tmf723 https://www.mathnet.ru/eng/tmf/v119/i1/p3
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Abstract page: | 564 | Full-text PDF : | 286 | References: | 80 | First page: | 3 |
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