Geodesic
Integral relations for special functions of hypergeometric and Heun class
Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 3, pp. 388-396 
A. Ya. Kazakov; S. Yu. Slavyanov. Integral relations for special functions of hypergeometric and Heun class. Teoretičeskaâ i matematičeskaâ fizika, Tome 107 (1996) no. 3, pp. 388-396. http://geodesic.mathdoc.fr/item/TMF_1996_107_3_a3/
@article{TMF_1996_107_3_a3,
     author = {A. Ya. Kazakov and S. Yu. Slavyanov},
     title = {Integral relations for special functions of hypergeometric and {Heun} class},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {388--396},
     year = {1996},
     volume = {107},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1996_107_3_a3/}
}
TY  - JOUR
AU  - A. Ya. Kazakov
AU  - S. Yu. Slavyanov
TI  - Integral relations for special functions of hypergeometric and Heun class
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1996
SP  - 388
EP  - 396
VL  - 107
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TMF_1996_107_3_a3/
LA  - ru
ID  - TMF_1996_107_3_a3
ER  - 
%0 Journal Article
%A A. Ya. Kazakov
%A S. Yu. Slavyanov
%T Integral relations for special functions of hypergeometric and Heun class
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1996
%P 388-396
%V 107
%N 3
%U http://geodesic.mathdoc.fr/item/TMF_1996_107_3_a3/
%G ru
%F TMF_1996_107_3_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

Ordinary differential equations with polynomial coefficients originate different kinds of integral relations for its solutions: integral representations in terms of simpler functions, integral equations etc. In this paper, a new kind of integral relations for functions of the Heun class are presented. These relations are coupling in ivolution eigensolutions, which are characterized by different behaviour at singularities and often also by different intervals of consideration and equations themselves. The studied relations are arranged in two staircases where each succeeding equation may be obtained with the help of the confluence process.

[1] A. Decarreau, M. C. Dumont-Lepage, P. Maroni, A. Robert, A. Ronveaux, Ann. Soc. Sc. de Brux., 92 (1978), 53–78 | MR | Zbl

[2] A. Ronveaux (ed.), Heun's Differential Equations, Oxford Univ. Press, 1995

[3] A. Ya. Kazakov, S. Yu. Slavyanov, Methods and Applications of Analysis (to appear)

[4] S. Yu. Slavyanov, W. Lay, A. Seeger, Heun's Differential Equation, Oxford Univ. Press, 1955 | MR

[5] S. Yu. Slavyanov, A. Zeeger, V. Lai, TMF, 104:2 (1995), 233–247 | MR | Zbl