Geodesic
Integral representations of $q$-Macdonald
Sbornik. Mathematics, Tome 194 (2003) no. 2, pp. 281-293 
V. K. Rogov. Integral representations of $q$-Macdonald. Sbornik. Mathematics, Tome 194 (2003) no. 2, pp. 281-293. http://geodesic.mathdoc.fr/item/SM_2003_194_2_a5/
@article{SM_2003_194_2_a5,
     author = {V. K. Rogov},
     title = {Integral representations of $q${-Macdonald}},
     journal = {Sbornik. Mathematics},
     pages = {281--293},
     year = {2003},
     volume = {194},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_2_a5/}
}
TY  - JOUR
AU  - V. K. Rogov
TI  - Integral representations of $q$-Macdonald
JO  - Sbornik. Mathematics
PY  - 2003
SP  - 281
EP  - 293
VL  - 194
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_2003_194_2_a5/
LA  - en
ID  - SM_2003_194_2_a5
ER  - 
%0 Journal Article
%A V. K. Rogov
%T Integral representations of $q$-Macdonald
%J Sbornik. Mathematics
%D 2003
%P 281-293
%V 194
%N 2
%U http://geodesic.mathdoc.fr/item/SM_2003_194_2_a5/
%G en
%F SM_2003_194_2_a5

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

$q$-Macdonald functions of the first, second, and third kinds are considered. Their representations by classical integrals are constructed.

[1] Olshanetskii M. A., Rogov V.-B. K., “Modifitsirovannye $q$-funktsii Besselya i $q$-funktsii Makdonalda”, Matem. sb., 187:10 (1996), 109–128 | MR

[2] Rogov V.-B. K., $q$-Bessel–Macdonald functions, Preprint ITEP-TH-56/00

[3] Olshanetskii M. A., Rogov V.-B. K., “$q$-integralnye predstavleniya modifitsirovannykh $q$-funktsii Besselya i $q$-funktsii Makdonalda”, Matem. sb., 188:8 (1997), 125–148 | MR

[4] Jackson F. H., “The application of basic numbers to Bessel's and Legendre's functions”, Proc. London Math. Soc. (2), 2 (1905), 192–220 | DOI

[5] Gasper Dzh., Rakhman M., Bazisnye gipergeometricheskie ryady, Mir, M., 1993 | MR | Zbl

[6] Beitmen A., Erdeii A., Vysshie transtsendentnye funktsii, t. 2, Nauka, M., 1966

[7] Ditkin V. A., Prudnikov A. P., Integralnye preobrazovaniya i operatsionnoe ischislenie, Fizmatgiz, M., 1961