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SOME APPLICATIONS OF q-DIFFERENTIAL OPERATOR

Jian-Ping Fang
대한수학회 (The Korean Mathematical Society)|2010.03|대한수학회지 (Journal of the KMS)|제47권 제2호|pp. 223-233

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참고문헌

키워드

q-seriesq-differential operatorRogers-Ramanujan type identity
주제분류수학

초록

In this paper, we use q-differential operator to recover the finite Heine 2Φ1 transformations given in [3]. Applying that, we also obtain some terminating q-series transformation formulas.

Abstract

In this paper, we use q-differential operator to recover the finite Heine 2Φ1 transformations given in [3]. Applying that, we also obtain some terminating q-series transformation formulas.

참고문헌 (15)

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  2. G. E. Andrews, "The Theory of Partitions, Encyclopedia of Mathematics and its Applications, Vol. 2" (1976), Addison-Wesley Publishing Co.
  3. G. E. Andrews, "The finite Heine transformation, Preprint", ~
  4. G. E. Andrews, "Ramanujan’s Lost Notebook, Part I" (2005), Springer
  5. G. E. Andrews, "The product of partial theta functions", Adv. in Appl. Math., 39(1), pp.116~120 (2007)
  6. J.-P. Fang, "A q-differential operator identity and its applications", J. East China Norm. Univ. Natur. Sci. Ed., 2008(1), pp.20~24 (2008)
  7. J.-P. Fang, "Extensions of q-Chu-Vandermonde’s identity", J. Math. Anal. Appl., 339(2), pp.845~852 (2008)
  8. G. Gasper, "Basic Hypergeometric Series" (1990), Cambridge University Press
  9. V. K. Jain, "Some transformations of basic hypergeometric series and their applications", Proc. Amer. Math. Soc., 78(3), pp.375~384 (1980)
  10. Z.-G. Liu, "An expansion formula for q-series and applications", Ramanujan J., 6(4), pp.429~447 (2002)
  11. Z.-G. Liu, "Some operator identities and q-series transformation formulas", Discrete Math., 265(1), pp.119~139 (2003)
  12. L. J. Rogers, "On the expansion of some infinte products", Proc. London Math. Soc., 통권 : 24, pp.337~352 (1893)
  13. A. V. Sills, "Finite Rogers-Ramanujan type identities", Electron. J. Combin., 10(13), pp.122~ (2003)
  14. L. J. Slater, "Further identies of the Rogers-Ramanujan type", Proc. London Math. Soc., 54(2), pp.147~167 (1952)
  15. S. O.Warnaar, "Partial theta functions. I. Beyond the lost notebook", Proc. London Math. Soc., 87(2), pp.363~395 (2003)

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