Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME APPLICATIONS OF q-DIFFERENTIAL OPERATOR

  • Fang, Jian-Ping (School of Mathematical Sciences, Huaiyin Normal University)
  • Published : 2010.03.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we use q-differential operator to recover the finite Heine $_2\Phi_1$ transformations given in [3]. Applying that, we also obtain some terminating q-series transformation formulas.

Keywords

References

  1. G. E. Andrews, Enumerative proofs of certain q-identities, Glasgow Math. J. 8 (1967), 33-40. https://doi.org/10.1017/S0017089500000057
  2. G. E. Andrews, The Theory of Partitions, Encyclopedia of Mathematics and its Applications, Vol. 2. Addison-Wesley Publishing Co., Reading, Mass.-London-Amsterdam, 1976.
  3. G. E. Andrews, The finite Heine transformation, Preprint.
  4. G. E. Andrews and B. C. Berndt, Ramanujan's Lost Notebook, Part I, Springer, 2005.
  5. G. E. Andrews and S. O. Warnaar, The product of partial theta functions, Adv. in Appl. Math. 39 (2007), no. 1, 116–120. https://doi.org/10.1016/j.aam.2005.12.003
  6. J.-P. Fang, A q-differential operator identity and its applications, J. East China Norm. Univ. Natur. Sci. Ed. 2008 (2008), no. 1, 20–24.
  7. J.-P. Fang, Extensions of q-Chu-Vandermonde's identity, J. Math. Anal. Appl. 339 (2008), no. 2, 845–852. https://doi.org/10.1016/j.jmaa.2007.07.029
  8. G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990.
  9. V. K. Jain, Some transformations of basic hypergeometric series and their applications, Proc. Amer. Math. Soc. 78 (1980), no. 3, 375–384. https://doi.org/10.2307/2042329
  10. Z.-G. Liu, An expansion formula for q-series and applications, Ramanujan J. 6 (2002), no. 4, 429–447. https://doi.org/10.1023/A:1021306016666
  11. Z.-G. Liu, Some operator identities and q-series transformation formulas, Discrete Math. 265 (2003), no. 1-3, 119–139. https://doi.org/10.1016/S0012-365X(02)00626-X
  12. L. J. Rogers, On the expansion of some infinte products, Proc. London Math. Soc. 24 (1893), 337–352. https://doi.org/10.1112/plms/s1-24.1.337
  13. A. V. Sills, Finite Rogers-Ramanujan type identities, Electron. J. Combin. 10 (2003), Research Paper 13, 122 pp.
  14. L. J. Slater, Further identies of the Rogers-Ramanujan type, Proc. London Math. Soc. (2) 54 (1952), 147–167. https://doi.org/10.1112/plms/s2-54.2.147
  15. S. O.Warnaar, Partial theta functions. I. Beyond the lost notebook, Proc. London Math. Soc. (3) 87 (2003), no. 2, 363–395. https://doi.org/10.1112/S002461150201403X

Cited by

  1. Remarks on a generalizedq-difference equation vol.21, pp.10, 2015, https://doi.org/10.1080/10236198.2015.1056176
  2. Two generalized q-exponential operators and their applications vol.2016, pp.1, 2016, https://doi.org/10.1186/s13662-016-0741-6
  3. Caputo type fractional difference operator and its application on discrete time scales vol.2015, pp.1, 2015, https://doi.org/10.1186/s13662-015-0496-5
  4. Applications of a generalized q-difference equation vol.2014, pp.1, 2014, https://doi.org/10.1186/1687-1847-2014-267
  5. A note on generalized q-difference equations for q-beta and Andrews–Askey integral vol.412, pp.2, 2014, https://doi.org/10.1016/j.jmaa.2013.11.027
  6. q-Difference equation and q-polynomials vol.248, 2014, https://doi.org/10.1016/j.amc.2014.10.010
  7. Generalizations of Milne’s U(n + 1) q-Chu-Vandermonde summation vol.66, pp.2, 2016, https://doi.org/10.1007/s10587-016-0263-0