Geodesic
Special functions in academician A. A. Dorodnicyn’s scientific legacy: Special functions arising in the solution of boundary value problems for second-order singular ordinary differential equations by asymptotic methods
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 1995-2032 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

On the occasion of the centenary of Academician A. A. Dorodnicyn’s birth, his main results concerning asymptotic methods for solving second-order singular ordinary differential equations and special functions related to these equations are presented (with certain corrections and additions). 
@article{ZVMMF_2011_51_11_a5,
     author = {M. K. Kerimov},
     title = {Special functions in academician {A.} {A.~Dorodnicyn{\textquoteright}s} scientific legacy: {Special} functions arising in the solution of boundary value problems for second-order singular ordinary differential equations by asymptotic methods},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1995--2032},
     year = {2011},
     volume = {51},
     number = {11},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a5/}
}
TY  - JOUR
AU  - M. K. Kerimov
TI  - Special functions in academician A. A. Dorodnicyn’s scientific legacy: Special functions arising in the solution of boundary value problems for second-order singular ordinary differential equations by asymptotic methods
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1995
EP  - 2032
VL  - 51
IS  - 11
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a5/
LA  - ru
ID  - ZVMMF_2011_51_11_a5
ER  - 
%0 Journal Article
%A M. K. Kerimov
%T Special functions in academician A. A. Dorodnicyn’s scientific legacy: Special functions arising in the solution of boundary value problems for second-order singular ordinary differential equations by asymptotic methods
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1995-2032
%V 51
%N 11
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a5/
%G ru
%F ZVMMF_2011_51_11_a5
M. K. Kerimov. Special functions in academician A. A. Dorodnicyn’s scientific legacy: Special functions arising in the solution of boundary value problems for second-order singular ordinary differential equations by asymptotic methods. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 11, pp. 1995-2032. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_11_a5/

[1] Dorodnitsyn A. A., “Asimptoticheskoe reshenie uravnenie Van der Polya”, Prikl. matem. i mekhan., 11:3 (1947), 343–328 ; Избранные научные труды, т. 1, ВЦ РАН, М., 1997, 40–59 | MR

[2] Dorodnitsyn A. A., “Asimptoticheskie zakony raspredeleniya sobstvennykh znachenii dlya nekotorykh osobykh vidov differentsialnykh uravnenii vtorogo poryadka”, Uspekhi matem. nauk, 7:6 (1952), 3–96

[3] Kerimov M. K., “Spetsialnye funktsii v nauchnom nasledii A. A. Dorodnitsyna. Spetsialnye funktsii, svyazannye s differentsialnym uravneniem Van der Polya”, Zh. vychisl. matem. i matem. fiz., 51:5 (2011), 834–857 | MR

[4] Kerimov M. K., “O nekotorykh spetsialnykh funktsiyakh, voznikayuschikh pri reshenii asimptoticheskimi metodami obyknovennykh differentsialnykh uravnenii”, Zh. vychisl. matem. i matem. fiz., 36:11 (1996), 80–101 | MR

[5] Petrashen M. I., “O poluklassicheskikh metodakh resheniya volnovogo uravneniya”, Uch. zap. LGU, 1949, no. 7, 59–78

[6] Horn J., “Über eine lineare Differentialgleichung Zweiter Ordnung mit einem willkurlichen Parameter”, Math. Ann., 52 (1899), 271–292 | DOI | MR | Zbl

[7] Langer R., “The asymptotic solutions of ordinary linear differential equations of the second order, with special reference to a turning point”, Trans. Amer. Math. Soc., 67:2 (1949), 197–270 | DOI | MR

[8] Olver F. W. J., Asymptotic and special functions, Acad. Press, London–New York, 1974 ; Olver F., Asimptotika i spetsialnye funktsii, ed. A. P. Prudnikov, Nauka, Fizmatlit, M., 1990 | MR | MR | Zbl

[9] Fedoryuk M. V., Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1983 | MR | Zbl