Geodesic
On generalized eighth order mock theta functions
Ural mathematical journal, Tome 6 (2020) no. 1, pp. 137-146 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper we have generalized eighth order mock theta functions, recently introduced by Gordon and MacIntosh involving four independent variables. The idea of generalizing was to have four extra parameters, which on specializing give known functions and thus these results hold for those known functions. We have represented these generalized functions as $q$-integral. Thus on specializing we have the classical mock theta functions represented as $q$-integral. The same is true for the multibasic expansion given.
Keywords: $q$-Hypergeometric series, Mock theta functions, Continued fractions, $q$-Integrals. 
@article{UMJ_2020_6_1_a10,
     author = {Pramod Kumar Rawat},
     title = {On generalized eighth order mock theta functions},
     journal = {Ural mathematical journal},
     pages = {137--146},
     year = {2020},
     volume = {6},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2020_6_1_a10/}
}
TY  - JOUR
AU  - Pramod Kumar Rawat
TI  - On generalized eighth order mock theta functions
JO  - Ural mathematical journal
PY  - 2020
SP  - 137
EP  - 146
VL  - 6
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UMJ_2020_6_1_a10/
LA  - en
ID  - UMJ_2020_6_1_a10
ER  - 
%0 Journal Article
%A Pramod Kumar Rawat
%T On generalized eighth order mock theta functions
%J Ural mathematical journal
%D 2020
%P 137-146
%V 6
%N 1
%U http://geodesic.mathdoc.fr/item/UMJ_2020_6_1_a10/
%G en
%F UMJ_2020_6_1_a10
Pramod Kumar Rawat. On generalized eighth order mock theta functions. Ural mathematical journal, Tome 6 (2020) no. 1, pp. 137-146. http://geodesic.mathdoc.fr/item/UMJ_2020_6_1_a10/

[1] Andrews G. E., “On basic hypergeometric series, mock theta functions and partitions (I)”, Q. J. Math., 17:2 (1966), 64–80 | DOI | MR | Zbl

[2] Andrews G. E., Berndt B. C., Ramanujan’s Lost Notebook, v. I, Springer-Verlag, New York, 2005, 437 pp. | DOI | MR

[3] Andrews G. E., Hickerson D., “Ramanujan’s “lost” notebook VII: The sixth order mock theta functions”, Adv. Math., 89:1 (1991), 60–105 | DOI | MR | Zbl

[4] Choi Y.-S., “The basic bilateral hypergeometric series and the mock theta functions”, Ramanujan J., 24 (2011), 345–386 | DOI | MR | Zbl

[5] Srinivasa Ramanujan, Collected Papers of Srinivasa Ramanujan, eds. Hardy G. H., Seshu Aiyar P. V., Wilson B. M., Chelsea Pub. Co., New York, 1962, 355 pp. | MR

[6] Gasper G., Rahman M., Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990, 276 pp. | MR | Zbl

[7] Gordon B., Macintosh R. J., “Some eighth order mock theta functions”, J. London Math. Soc., 62:2 (2000), 321–335 | DOI | MR | Zbl

[8] Jackson F. H., “Basic Integration”, Q. J. Math., 2:1 (1951), 1–16 | DOI | MR | Zbl

[9] Rainville E. D., Special Function, Chelsea Pub. Co., New York, 1960, 365 pp. | MR

[10] Sills A. V., An Invitation to the Rogers-Ramanujan Identities, Chapman and Hall/CRC, New York, 2017, 256 pp. | DOI | MR

[11] Srivastava B., “A generalization of the eighth order mock theta functions and their multibasic expansion”, Saitama Math. J., 24 (2006/2007), 1–13 | MR

[12] Watson G. N., “The final problem: An account of the mock theta functions”, J. London Math. Soc., 11 (1936), 55–80 | DOI | MR