Geodesic
A regularization technique for computing the hypergeometric function $F(a,b;c;z)$in the neighborhood of the singular points $z=1$ and $z=\infty$
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 41 (2001) no. 12, pp. 1808-1832 
S. L. Skorokhodov. A regularization technique for computing the hypergeometric function $F(a,b;c;z)$in the neighborhood of the singular points $z=1$ and $z=\infty$. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 41 (2001) no. 12, pp. 1808-1832. http://geodesic.mathdoc.fr/item/ZVMMF_2001_41_12_a1/
@article{ZVMMF_2001_41_12_a1,
     author = {S. L. Skorokhodov},
     title = {A regularization technique for computing the hypergeometric function $F(a,b;c;z)$in the neighborhood of the singular points $z=1$ and $z=\infty$},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1808--1832},
     year = {2001},
     volume = {41},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2001_41_12_a1/}
}
TY  - JOUR
AU  - S. L. Skorokhodov
TI  - A regularization technique for computing the hypergeometric function $F(a,b;c;z)$in the neighborhood of the singular points $z=1$ and $z=\infty$
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2001
SP  - 1808
EP  - 1832
VL  - 41
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2001_41_12_a1/
LA  - ru
ID  - ZVMMF_2001_41_12_a1
ER  - 
%0 Journal Article
%A S. L. Skorokhodov
%T A regularization technique for computing the hypergeometric function $F(a,b;c;z)$in the neighborhood of the singular points $z=1$ and $z=\infty$
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2001
%P 1808-1832
%V 41
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2001_41_12_a1/
%G ru
%F ZVMMF_2001_41_12_a1

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

[1] Golubev V. V., Lektsii po analiticheskoi teorii differentsialnykh uravnenii, Gostekhteorizdat, M.–L., 1950

[2] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii. Gipergeometricheskaya funktsiya. Funktsiya Lezhandra, Nauka, M., 1973

[3] Uitteker E. T., Vatson Dzh. N., Kurs sovremennogo analiza, v. II, Fizmatgiz, M., 1963

[4] Krattser A., Frants V., Transtsendentnye funktsii, Izd-vo inostr. lit., M., 1963

[5] Henrici P., Applied and computational complex analysis, v. I, J. Willey Sons, New York, 1988 ; v. II, 1991 | MR | Zbl | Zbl

[6] Temme N. M., Special functions. An introduction to the classical functions of mathematical physics, J. Willey Sons, New York, 1996 | MR | Zbl

[7] Olver F. W. J., Asymptotics and special functions, Acad. Press, New York, 1974 | MR

[8] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1987 | MR

[9] Forrey R. C., “Computing the hypergeometric function”, J. Comput. Phys., 137:1 (1997), 79–100 | DOI | MR | Zbl

[10] Bourguet L., “Sur les integrales Euleriennes et quelques autres fonctions uniformes”, Acta Math., 2 (1883), 261–295 | DOI | MR

[11] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam, Nauka, M., 1979 | MR

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

[13] Wrench J. W., “Concerning two series for the Gamma function”, Math. Comput., 22:103 (1968), 617–626 ; Errata, Math. Comput., 27:123 (1973), 681–682 | DOI | MR | Zbl | MR

[14] Nielsen N., Die Gammafunktion, v. I, Handbuch der Theorie der Gammafunktion, Chelsea, New York, 1965

[15] Spira R., “Calculation of the Gamma function by Stirling's formula”, Math. Comput., 25:114 (1971), 317–322 | MR | Zbl

[16] Frenzen C. L., “Error bounds for the asymptotic expansion of the ratio of two Gamma functions with complex argument”, SIAM J. Math. Analys., 23:2 (1992), 505–511 | DOI | MR | Zbl

[17] Gautschi W., “Computational aspects of three-term recurrence relations”, SIAM Rev., 9:1 (1967), 24–82 | DOI | MR | Zbl

[18] Olver F. W. J., Sookne D. J., “Note on backward recurrence algorithms”, Math. Comput., 26:120 (1974), 941–947 | MR

[19] Zahar R. V. M., “A mathematical analysis of Miller's algorithm”, Numer. Math., 27 (1977), 427–447 | DOI | MR | Zbl

[20] Kerimov M. K., Skorokhodov S. L., “O vychislenii modifitsirovannykh funktsii Besselya v kompleksnoi oblasti”, Zh. vychisl. matem. i matem. fiz., 24:5 (1984), 650–664 | MR | Zbl