Geodesic
On the theory of special functions and their approximations
Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 429-458 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For general nonhomogeneous linear equations with one regular singular point, the questions of solvability, the structure of the corresponding Wronskians, and the Cauchy–Green functions are studied on a finite interval. Formulas for the resolvents of the resulting integral equations are obtained in explicit form. An effective method of constructing differential equations for the analytic parts of special functions is indicated, and an analytical method is worked out for their best asymptotic approximation, which at the same time gives a high degree of accuracy in their practical computation on computers. Bibliography: 17 titles. 
@article{SM_1988_59_2_a10,
     author = {V. K. Dzyadyk},
     title = {On the theory of special functions and their approximations},
     journal = {Sbornik. Mathematics},
     pages = {429--458},
     year = {1988},
     volume = {59},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1988_59_2_a10/}
}
TY  - JOUR
AU  - V. K. Dzyadyk
TI  - On the theory of special functions and their approximations
JO  - Sbornik. Mathematics
PY  - 1988
SP  - 429
EP  - 458
VL  - 59
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1988_59_2_a10/
LA  - en
ID  - SM_1988_59_2_a10
ER  - 
%0 Journal Article
%A V. K. Dzyadyk
%T On the theory of special functions and their approximations
%J Sbornik. Mathematics
%D 1988
%P 429-458
%V 59
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1988_59_2_a10/
%G en
%F SM_1988_59_2_a10
V. K. Dzyadyk. On the theory of special functions and their approximations. Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 429-458. http://geodesic.mathdoc.fr/item/SM_1988_59_2_a10/

[1] Dzyadyk V. K., “Approksimatsionnyi metod priblizheniya algebraicheskimi mnogochlenami reshenii lineinykh differentsialnykh uravnenii”, Izv. AN SSSR. Ser. matem., 38 (1974), 937–967 | Zbl

[2] Stolyarchuk V. K., “O ravnomernom priblizhenii funktsii Besselya s tselym indeksom mnogochlenami”, Ukr. matem. zhurn., 26:5 (1974), 670–674

[3] Stolyarchuk V. K., “O postroenii dlya funktsii $\operatorname{si}x$ i $\Phi(x)=\frac{2}{\sqrt{\pi}}\int_0^xe^{-t^2}\,dt$ mnogochlenov, kotorye osuschestvlyayut ikh priblizhenie, blizkoe k nailuchshemu”, Ukr. matem. zhurn., 26:2 (1974), 215–224

[4] Stolyarchuk V. K., “O ravnomernom priblizhenii mnogochlenami na segmente gipergeometricheskikh funktsii”, Voprosy teorii priblizheniya funktsii i ee prilozhenii, Kiev, 1976, 179–185

[5] Gelfond A. O., Ischislenie konechnykh raznostei, Nauka, M., 1967 | MR

[6] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl

[7] Gursa E., Kurs matematicheskogo analiza, t. II, M.-L., 1936

[8] Lyuk Yu., Spetsialnye matematicheskie funktsii i ikh approksimatsii, Mir, M., 1980

[9] Abramovits M., Stigan I., Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979 | MR

[10] Aigner M., Kombinatornaya teoriya, Mir, M., 1982 | MR

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

[12] Koddington E. A., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, IL, M., 1958

[13] Markov A. A., Izbrannye trudy, M.-L., 1948

[14] Bernshtein S. N., Ob odnom klasse ortogonalnykh mnogochlenov, Sobr. soch., t. 1, 1952, 452–467

[15] Akhiezer N. I., Lektsii po teorii approksimatsii, Nauka, M., 1966, 290–294 | Zbl

[16] Dzyadyk V. K., “On a problem of Chebyshev and Markov”, Analysis Math., 3.3 (1977), 171–175 | DOI | Zbl

[17] Pashkovskii S., Vychislitelnye primeneniya mnogochlenov i ryadov Chebysheva, Nauka, M., 1983 | MR