TY - JOUR

T1 - Structural theory of special functions

AU - Slavyanov, S. Yu

PY - 1999/1/1

Y1 - 1999/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033244320&partnerID=8YFLogxK

U2 - 10.1007/BF02557338

DO - 10.1007/BF02557338

M3 - Article

AN - SCOPUS:0033244320

VL - 119

SP - 393

EP - 406

JO - Theoretical and Mathematical Physics (Russian Federation)

JF - Theoretical and Mathematical Physics (Russian Federation)

SN - 0040-5779

IS - 1

ER -