Geodesic
Confluent Heun equation and confluent hypergeometric equation
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVIII, Tome 462 (2017), pp. 93-102 
S. Yu. Slavyanov; A. A. Salatich. Confluent Heun equation and confluent hypergeometric equation. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXVIII, Tome 462 (2017), pp. 93-102. http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a4/
@article{ZNSL_2017_462_a4,
     author = {S. Yu. Slavyanov and A. A. Salatich},
     title = {Confluent {Heun} equation and confluent hypergeometric equation},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {93--102},
     year = {2017},
     volume = {462},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a4/}
}
TY  - JOUR
AU  - S. Yu. Slavyanov
AU  - A. A. Salatich
TI  - Confluent Heun equation and confluent hypergeometric equation
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 93
EP  - 102
VL  - 462
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a4/
LA  - ru
ID  - ZNSL_2017_462_a4
ER  - 
%0 Journal Article
%A S. Yu. Slavyanov
%A A. A. Salatich
%T Confluent Heun equation and confluent hypergeometric equation
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 93-102
%V 462
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_462_a4/
%G ru
%F ZNSL_2017_462_a4

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The confluent Heun equation and confluent hypergeometric equation are studied in scalar and vector forms with particular emphasis to the role of apparent singularities. The relation to the Painlevé equation is shown.

[1] A. Kazakov, S. Slavyanov, “Integralnye simmetrii Eilera dlya konflyuentnogo uravneniya Goina i simmetrii uravneniya Penleve $P^V$”, Teor. mat. fiz., 179:2 (2014), 189–195 | DOI | MR | Zbl

[2] S. Slavyanov, “Simmetrii i lozhnye singulyarnosti dlya prosteishikh fuksovykh uravnenii”, Teor. mat. fiz., 193:3 (2017), 401–408 | DOI

[3] S. Slavyanov, V. Lai, Spetsialnye funktsii: edinaya teoriya, osnovannaya na analize singulyarnostei, Nevskii dialekt, SPb., 2002

[4] A. Ronveaux (ed.), Heun's Differential Equation, Oxford Univ. Press, Oxford–New York–Tokyo, 1995

[5] S. Slavyanov, D. Shatko, A. Ishkanyan, T. Rotinyan, “Generatsiya i udalenie lozhnykh osobennostei v lineinykh ODU s polinomialnym koeffitsientom”, Teor. mat. fiz., 189:3 (2016), 371–379 | DOI | MR | Zbl

[6] S. Slavyanov, “Antikvantovanie i sootvetstvuyuschie simmetrii”, Teor. mat. fiz., 182:2 (2015), 223–230 | DOI | MR | Zbl

[7] S. Yu. Slavyanov, O. L. Stesik, “Antikvantovanie deformirovannykh uravnenii klassa Goina”, Teor. mat. fiz., 186:1 (2016), 142–151 | DOI | MR | Zbl

[8] A. Ishkhanyan, K. Suominen, “New solutions of Heun's general equation”, J. Phys. A, 36 (2003), L81–L86 | DOI | MR

[9] A. D. Bruno, A. B. Batkin (eds.), Painlevé Equations and Related Topics, De Gruyter, 2012 | MR

[10] S. Yu. Slavyanov, “Painlevé equations as classical analogues of Heun equation”, J. Phys. A, 29 (1996), 7329–7335 | DOI | MR | Zbl