Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Resonance of Continued Fractions Related to 2ψ2Basic Bilateral Hypergeometric Series

  • Srivastava, Pankaj (Department of Mathematics, Motilal Nehru National Institute of Technology)
  • Received : 2010.08.17
  • Accepted : 2011.04.26
  • Published : 2011.11.23
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Abstract

In this paper, making use of transformation due to S. N. Singh [21], an at-tempt has been made to establish certain results involving basic bilateral hypergeometric series and continued fractions.

Keywords

References

  1. R. P. Agarwal, Resonance of Ramanujan's mathematics Vol. III, New Age International Pvt. Ltd. Publishers, New Delhi, 1998.
  2. G. E. Andrews, Ramanujan's `Lost'Note Book III, The Rogers-Ramanujan's continued fraction, Adv. Math., 2, 41(1981), 186-208. https://doi.org/10.1016/0001-8708(81)90015-3
  3. C. Adiga, D. D. Somashekara, On some Rogers-Ramanujan type continued fraction identities, Mathematica Balkamica, New Series 1-2, 12(1998), 37-45.
  4. C. Adiga, D. D. Somashekara, Rogers-Ramanujan Identities, continued fractions and their generalizations, Selected Topics in Special Functions, Allied publisher limited , 2001, 208-226.
  5. N. A. Bhagirathi, On certain investigations in q-series and continued fractions, Math. Student, 1-4, 56(1988), 158-170.
  6. N. A. Bhagirathi, On basic bilateral hypergeometric series and continued fractions, Math. Student, 1-4, 56(1988), 135-141.
  7. B. C. Berndt, Ramanujan's Notebook part III, Springer-Verlag, 1991.
  8. S. Bhargava, C. Adiga, D. D. Somashekara, On certain continued fractions related to $3\phi2$ basic hypergeometric functions, J. Math. Phys. Sci., 21(1987), 613-629.
  9. S. Bhargava, C. Adiga, On some continued fraction of Srinivas Ramanujan, Proc. Amer. Math. Soc., 92(1984), 13-18. https://doi.org/10.1090/S0002-9939-1984-0749881-3
  10. R. Y. Denis, On basic hypergeometric function and continued fractions, Math. Student, 1-4, 52(1984), 129-136.
  11. R. Y. Denis, On certain q-series and continued fractions, Math. Student, 44(1983), 70-76.
  12. R. Y. Denis, On certain continued fraction of Ramanujan, Jour. Math. Phy. Sci., 3, 24(1990), 193-205.
  13. R. Y. Denis, On generalization of Euler's continued fraction, Indian J. Pure Appl. Math., 21(1)(1990), 78-81.
  14. M. D. Hirschhorn, A continued fraction of Ramanujan, J. Australian Math. Soc., 29(1980), 80-86. https://doi.org/10.1017/S1446788700020954
  15. Kline, Morris, Mathematical thought from ancient to modern time, Oxford Univ. Press, 1972, 28-32.
  16. Maheshwar Pathak and Pankaj Srivastava, A note on continued fractions and 3 3 series, Italian J. Pure Appl. Math., 27(2010), 191-200.
  17. S. Ramanujan, Note book of Ramanujan Vol. I & II, T. I. F. R. Bombay, 1957.
  18. S. Ramanujan, The lost note book and other unpublished papers, Narosa, New Delhi, 1988.
  19. S. N. Singh, On q-hypergeometric function and continued fractions, Math. Student, 1-4, 56(1988), 81-84.
  20. S. N. Singh, Basic hypergeometric series and continued fractions, Math. Student, 1-4, 56(1988), 91-96.
  21. S. N. Singh, Certain transformation formulae for basic and bibasic hypergeometric series, Proc. Nat. Acad. Sci. India, 65(A), III(1995), 319-329.
  22. Pankaj Srivastava, Certain continued fractions for quotients of two 3 3 series , Proc. Nat. Acad. Sci. India, 78(A), IV(2008), 327-330.
  23. Bhaskar Srivastava, A continued fraction and some identities associated with Ramanujan, Riv. Math. Univ. Parma., 17(1991), 199-206.
  24. L. C. Zhang, Ramanujan's continued fraction for product of gamma functions, J. Math. Anal. Appli., 174(1993), 22-25. https://doi.org/10.1006/jmaa.1993.1100

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