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ON SOME PARTIAL THETA FUNCTION IDENTITIES OF RAMANUJAN FOUND IN HIS LOST NOTEBOOK

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Ramanujan has recorded several identities involving partial theta functions in his lost notebook. In 1981, Andrews has given proofs for sixteen of those identities by employing his general identity. In this paper, we obtain ten of those identities by an alternate method. We also deduce several interesting special cases.

Abstract

Ramanujan has recorded several identities involving partial theta functions in his lost notebook. In 1981, Andrews has given proofs for sixteen of those identities by employing his general identity. In this paper, we obtain ten of those identities by an alternate method. We also deduce several interesting special cases.

참고문헌 (21)

  1. C. Adiga, "On a reciprocity theorem of Ramanujan", Tamsui J. Math. Sci, 22, pp.9~15 (2006)
  2. R. P. Agarwal, "On the paper, "A `lost notebook of Ramanujan"", Adv. in Math, 53, pp.291~300 (1984)
  3. G. E. Andrews, "Ramanujan's `lost' notebook. I. partial -functions", Adv. in Math, 41, pp.137~172 (1981)
  4. G. E. Andrews, "Special functions" (1999), Cambridge University Press
  5. G. E. Andrews, "Ramanujan's Lost Notebook, Part II" (2009), Springer
  6. B. C. Berndt, "Ramanujan's Notebooks, Part III" (1991), Springer-Verlag
  7. B. C. Berndt, "A reciprocity theorem for certain q-series found in Ramanujan's lost notebook", Ramanujan J, 13, pp.27~37 (2007)
  8. S. Bhargava, "Some q-Gamma and q-Beta function identities deducible from the reciprocity theorem of Ramanujan", Adv. Stud. Contemp. Math, 11, pp.227~234 (2005)
  9. G. Gasper, "Basic hypergeometric series, Encyclopedia of Mathematics" (2004), Cambridge University press
  10. P. S. Guruprasad, "A simple proof of Ramanujan's reciprocity theorem", Proc. Jangjeon Math. Soc, 9, pp.121~124 (2006)
  11. Husam L. Saad, "The q-Exponential Operator", Applied Mathematical Sciences, 7(128), pp.6369~6380 (2013)
  12. C. G. J. Jacobi, "Sumptibus Fratrum Borntrager" (1829), Regiomonti
  13. S.-Y. Kang, "Generalizations of Ramanujan's reciprocity theorem and their applications", J. London Math. Soc, 75, pp.18~34 (2007)
  14. T. Kim, "On a generalization of Jacobi's triple product identity and its application", Adv. Stud. Contemp. Math, 9, pp.165~174 (2004)
  15. S. Ramanujan, "Notebooks (2 Volumes)" (1957), Tata Institute of Fundamental Research
  16. S. Ramanujan, "The lost notebook and other unpublished papers" (1988), Narosa
  17. L. J. Rogers, "Second memior on the expansion of certain in nite products", Proc. London Math. Soc, 25, pp.318~343 (1894)
  18. D. D. Somashekara, "An interesting generalization of Jacobi's triple product identity", Far East J. Math. Sci, 9, pp.255~259 (2003)
  19. D.D. Somashekara, "On some identities of Ramanujan found in his lost notebook", Advanced Studies in Contemporary Mathematics, 16(2), pp.171~180 (2008), 장전수학회
  20. D. D. Somashekara, "On A Two Variable reciprocity theorem Of Ramanujan Bull", Pure Appl. Math, 5(1), pp.75~78 (2011)
  21. D. D. Somashekara, "On the reciprocity theorem of Ramanujan and its generalizations", Proc. Jangjeon Math. Soc, 15(3), pp.343~353 (2012)

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