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A Note on Certain Properties of Mock Theta Functions of Order Eight

Pankaj Srivastava|Anwar Jahan Wahidi
경북대학교 자연과학대학 수학과|2014.06|Kyungpook Mathematical Journal|제54권 제2호|pp. 249-262|DOI http://dx.doi.org/10.5666/KMJ.2014.54.2.249

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참고문헌

키워드

q-difference equationBasic Hypergeometric seriesMock Theta Functions
주제분류수학

초록

In this paper, we have developed a non-homogeneous q- difference equation of first order for the generalizedMock 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 numberof cases of the identities.

Abstract

In this paper, we have developed a non-homogeneous q- difference equation of first order for the generalizedMock 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 numberof cases of the identities.

참고문헌 (22)

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  2. G. E. Andrews, "On basic hypergeometric series, Mock theta functions and partitions (II)", Quart. J. Math. Oxford Ser., 17, pp.132~143 (1966)
  3. R. P. Agarwal, "Resonance of Ramanujan's Mathematics II" (1995), New Age International Pvt. Ltd. Publishers
  4. R. P. Agarwal, "Resonance of Ramanujan's Mathematics III" (1998), New Age International Pvt. Ltd. Publishers
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  6. R. P. Agarwal, "An attempt towards presenting an unified theory for mock theta functions", Proc. Int. Conf. SSFA, 1, pp.11~19 (2001)
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  8. R. Y. Denis, "On certain expansions of basic hypergeometric function and q-fractional derivatives", Ganita, 38, pp.91~100 (1987)
  9. R. Y. Denis, "Certain representation of mock theta functions of order six and ten", Vikram Mathematical Journal, 18, pp.1~15 (1998)
  10. R. Y. Denis, "On certain new representation of mock theta functions", Italian J. Pure Appl. Math., 22, pp.149~154 (2007)
  11. G. Gasper, "Basic Hypergeometric Series" (1990), Cambridge University Press
  12. B. Gordon, "Some eighth order Mock Theta Functions", J. London Math. Soc., 62(2), pp.321~335 (2000)
  13. Anju Gupta, "On Certain Ramanujan's Mock Theta functions", Proc. Indian Acad. Sci.(Math. Sci.), 3(103), pp.257~267 (1993)
  14. Anju Gupta, "A Study of certain basic hypergeometric functions and transformations associated with Ramanujan", Doctor, pp.1992
  15. K. Hikami, "Transformation formula of the 2nd order Mock theta functions", Lett. Math. Phys., 75, pp.93~98 (2006)
  16. S. D. Prasad, "Certain extended Mock Theta functions and generalized basic hyperge-ometric transformations", Math. Scand., 27, pp.237~244 (1970)
  17. A. K. Srivastava, "On partial sum of mock theta functions of order three", Proc. Indian. Acad. Sci, 107, pp.1~12 (1997)
  18. Bhaskar Srivastava, "Mock Theta Functions and Theta Functions", New Zealand Jour-nal of Mathematics, 36, pp.287~294 (2007)
  19. Pankaj Srivastava, "A note on Hikami's Mock theta func-tions", Int. Journal of Math. Analysis, 43(5), pp.2103~2109 (2011)
  20. Pankaj Srivastava, "Certain Generating Functions for Par-tial Mock Theta Functions of Order Two and Order Ten", Int. J. Contemp. Math. Sciences, 17(7), pp.839~848 (2012)
  21. Pankaj Srivastava, "A New Spectrum of Mock Theta Func-tions of Order Two", Journal of Inequalities and Special Functions, 4(3), pp.59~66 (2013)
  22. G. N. Watson, "A final problem: an account of the mock theta functions", J. London Math. Soc., 11, pp.55~80 (1936)

관련 논문AI추천

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