JOURNAL BROWSE
Search
Advanced SearchSearch Tips
A Note on Certain Properties of Mock Theta Functions of Order Eight
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
  • Journal title : Kyungpook mathematical journal
  • Volume 54, Issue 2,  2014, pp.249-262
  • Publisher : Department of Mathematics, Kyungpook National University
  • DOI : 10.5666/KMJ.2014.54.2.249
 Title & Authors
A Note on Certain Properties of Mock Theta Functions of Order Eight
Srivastava, Pankaj; Wahidi, Anwar Jahan;
  PDF(new window)
 Abstract
In this paper, we have developed a non-homogeneous q-difference equation of first order for the generalized Mock theta function of order eight and besides these established limiting case of Mock theta functions of order eight. We have also established identities for Partial Mock theta function and Mock theta function of order eight and provided a number of cases of the identities.
 Keywords
Mock Theta Functions;Basic Hypergeometric series;q-difference equation;
 Language
English
 Cited by
 References
1.
G. E. Andrews, On basic hypergeometric series, Mock theta functions and partitions(I), Quart. J. Math. Oxford Ser., 17(1966), 64-80. crossref(new window)

2.
G. E. Andrews, On basic hypergeometric series, Mock theta functions and partitions(II), Quart. J. Math. Oxford Ser., 17(1966), 132-143. crossref(new window)

3.
R. P. Agarwal, Resonance of Ramanujan's Mathematics II, New Age International Pvt. Ltd. Publishers, New Delhi, 1995.

4.
R. P. Agarwal, Resonance of Ramanujan's Mathematics III, New Age International Pvt. Ltd. Publishers, New Delhi, 1998.

5.
R. P. Agarwal, Mock Theta Functions- an analytical point of view, Proc. Nat. Acad. Sci., (India) 64(1994), 95-107.

6.
R. P. Agarwal, An attempt towards presenting an unified theory for mock theta functions Proc. Int. Conf. SSFA, 1(2001), 11-19

7.
Y. S. Choi, Tenth Order Mock Theta Functions in Ramanujan's Lost Notebook Invent. Math., 136(1999), 497-569. crossref(new window)

8.
R. Y. Denis, On certain expansions of basic hypergeometric function and q-fractional derivatives, Ganita, 38(1987), 91-100.

9.
R. Y. Denis and S. N. Singh, Certain representation of mock theta functions of order six and ten, Vikram Mathematical Journal, 18(1998), 1-15.

10.
R. Y. Denis, S. N. Singh and S. P. Singh, On certain new representation of mock theta functions, Italian J. Pure Appl. Math., 22(2007), 149-154.

11.
G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, New York, 1990.

12.
B. Gordon and R. J. McIntosh, Some eighth order Mock Theta Functions, J. London Math. Soc., 62(2)(2000), 321-335. crossref(new window)

13.
Anju Gupta, On Certain Ramanujan's Mock Theta functions, Proc. Indian Acad. Sci.(Math. Sci.), 3(103)(1993), 257-267.

14.
Anju Gupta, A Study of certain basic hypergeometric functions and transformations associated with Ramanujan, Doctoral Thesis, University of Lucknow (1992).

15.
K. Hikami, Transformation formula of the 2nd order Mock theta functions, Lett. Math. Phys., 75(2006), 93-98. crossref(new window)

16.
S. D. Prasad, Certain extended Mock Theta functions and generalized basic hyperge-ometric transformations, Math. Scand., 27(1970), 237-244.

17.
A. K. Srivastava, On partial sum of mock theta functions of order three, Proc. Indian. Acad. Sci., 107(1997), 1-12. crossref(new window)

18.
Bhaskar Srivastava, Mock Theta Functions and Theta Functions, New Zealand Journal of Mathematics, 36(2007), 287-294.

19.
Pankaj Srivastava and Anwar Jahan Wahidi, A note on Hikami's Mock theta functions, Int. Journal of Math. Analysis, 43(5)(2011), 2103-2109.

20.
Pankaj Srivastava and Anwar Jahan Wahidi, Certain Generating Functions for Partial Mock Theta Functions of Order Two and Order Ten, Int. J. Contemp. Math. Sciences, 17(7)(2012), 839-848.

21.
Pankaj Srivastava and Anwar Jahan Wahidi, A New Spectrum of Mock Theta Functions of Order Two, Journal of Inequalities and Special Functions, 4(3)(2013), 59-66.

22.
G. N. Watson, A final problem: an account of the mock theta functions, J. London Math. Soc., 11(1936), 55-80.