CERTAIN RELATIONS FOR MOCK THETA FUNCTIONS OF ORDER EIGHT

- Journal title : Communications of the Korean Mathematical Society
- Volume 24, Issue 4, 2009, pp.629-640
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2009.24.4.629

Title & Authors

CERTAIN RELATIONS FOR MOCK THETA FUNCTIONS OF ORDER EIGHT

Pathak, Maheshwar; Srivastava, Pankaj;

Pathak, Maheshwar; Srivastava, Pankaj;

Abstract

The aim of the present paper is to establish certain relations for partial mock theta functions and mock theta functions of order eight with other partial mock theta functions and mock theta functions of order two, six, eight and ten respectively.

Keywords

mock theta functions;continued fractions;basic hypergeometric series;

Language

English

References

1.

R. P. Agarwal, Resonance of Ramanujan's Mathematics II, New Age International Pvt. Ltd. Publishers, New Delhi, 1996

2.

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

3.

R. P. Agarwal, Pade approximants, continued fractions and Heine's q-hypergeometric series, J. Math. Phys. Sci. 26 (1992), no. 3, 281–290

4.

G. E. Andrew and D. Hickerson, Ramanujan's 'Lost' Notebook VII: The sixth order mock theta functions, Adv. Math. 89 (1991), 60–105

5.

Y. S. Choi, Tenth order mock theta functions in Ramanujan's lost notebook, Invent Math. 136 (1999), 497–569

6.

R. Y. Denis, S. N. Singh, and S. P. Singh, On certain relation connecting mock theta functions, Ital. J. Pure Appl. Math. 19 (2006), 55–60

7.

B. Gordon and R. J. McIntosh, Some eight order mock theta functions, J. Lond. Math. Soc. 62 (2000), 321–335

8.

S. Ramanujan, The Lost Notebook and Other Unpublished Papers, Narosa Publishing House, New Delhi, 1988

9.

S. N. Singh, Basic hypergeometric series and continued fractions, Math. Student 56 (1988), 91–96

10.

A. K. Srivastava, On partial sum of mock theta functions of order three, Proc. Indian Acad. Sci. Math. Sci. 107 (1997), 1–12

11.

B. Srivastava, Ramanujan's mock theta functions, Math. J. Okayama Univ. 47 (2005), no. 1, 163–174