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Resonance of Continued Fractions Related to 2ψ2 Basic Bilateral Hypergeometric Series

Pankaj Srivastava
경북대학교 자연과학대학 수학과|2011.12|Kyungpook Mathematical Journal|제51권 제4호|pp. 419-427

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참고문헌

키워드

Basic hypergeometric seriescontinued fractionsbasic bilateral series
주제분류수학

초록

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

Abstract

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

참고문헌 (24)

  1. R. P. Agarwal, "Resonance of Ramanujan's mathematics Vol. III" (1998), New Age Interna-tional Pvt. Ltd. Publishers
  2. G. E. Andrews, "Ramanujan's `Lost'Note Book III, The Rogers-Ramanujan's continued fraction", Adv. Math, 41(2), pp.186~208 (1981)
  3. C. Adiga, "On some Rogers-Ramanujan type continued fraction identities", Mathematica Balkamica, 12(1), pp.37~45 (1998)
  4. C. Adiga, "Rogers-Ramanujan Identities, continued fractions and their generalizations, Selected Topics in Special Functions", pp.208~226 (2001), Allied publisher limited
  5. N. A. Bhagirathi, "On certain investigations in q-series and continued fractions", Math. Student, 56(1), pp.158~170 (1988)
  6. N. A. Bhagirathi, "On basic bilateral hypergeometric series and continued fractions", Math. Student, 56(1), pp.135~141 (1988)
  7. B. C. Berndt, "Ramanujan's Notebook part III" (1991), Springer-Verlag
  8. S. Bhargava, "On certain continued fractions related to 3ϕ2 basic hypergeometric functions", J. Math. Phys. Sci, 21, pp.613~629 (1987)
  9. S. Bhargava, "On some continued fraction of Srinivas Ramanujan", Proc. Amer. Math. Soc, 92, pp.13~18 (1984)
  10. R. Y. Denis, "On basic hypergeometric function and continued fractions", Math. Stu-dent, 52(1), pp.129~136 (1984)
  11. R. Y. Denis, "On certain q-series and continued fractions", Math. Student, 44, pp.70~76 (1983)
  12. R. Y. Denis, "On certain continued fraction of Ramanujan", Jour. Math. Phy. Sci, 24(3), pp.193~205 (1990)
  13. R. Y. Denis, "On generalization of Euler's continued fraction", Indian J. Pure Appl. Math, 21(1), pp.79~81 (1990)
  14. M. D. Hirschhorn, "A continued fraction of Ramanujan", J. Australian Math. Soc, 29, pp.80~86 (1980)
  15. Kline, Morris, "Mathematical thought from ancient to modern time", pp.28~32 (1972), Oxford Univ. Press
  16. Maheshwar Pathak, "A note on continued fractions and 3 3 series", Italian J. Pure Appl. Math, 27, pp.194~200 (2010)
  17. S. Ramanujan, "Note book of Ramanujan Vol. I & II" (1957), T. I. F. R. Bombay
  18. The lost note book and other unpublished papers, "S. Ramanujan", Narosa, ~ (1988)
  19. S. N. Singh, "On q-hypergeometric function and continued fractions", Math. Student, 56(1), pp.81~84 (1988)
  20. S. N. Singh, "Basic hypergeometric series and continued fractions", Math. Student, 56(1), pp.91~96 (1988)
  21. S. N. Singh, "Certain transformation formulae for basic and bibasic hypergeometric series", Proc. Nat. Acad. Sci. India, 65(A)통권 : 3, pp.319~329 (1995)
  22. Pankaj Srivastava, "Certain continued fractions for quotients of two 3 3 series", Proc. Nat. Acad. Sci. India, 78(A)통권 : 4, pp.327~330 (2008)
  23. Bhaskar Srivastava, "A continued fraction and some identities associated with Ramanu-jan", Riv. Math. Univ. Parma, 17, pp.199~206 (1991)
  24. L. C. Zhang, "Ramanujan's continued fraction for product of gamma functions", J. Math. Anal. Appli, 174, pp.22~25 (1993)

관련 논문AI추천

On Certain Continued Fractions Related To 3ψ3 Basic Bilateral Hypergeometric FunctionsAbdulrawf A. A. Kahtan, G. Sharath, K. R. Vasuki장전수학회 · Advanced Studies in Contemporary Mathematics2010 · 제20권 제3호On certain transformations of basic hypergeometric functionsR. Y. Denis, S. N. Singh, S. P. Singh장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2007 · 제10권 제2호On certain continued fraction expansions for ratios of basic hypergeometric seriesK. R. Rajanna, K. R. Vasuki장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2007 · 제10권 제2호A new summation formula for basic bilateral hypergeometric series by 2φ2-exponential operator techniqueADITYA AGNIHOTRI, S. Ahmad Ali장전수학회 · Advanced Studies in Contemporary Mathematics2019 · 제29권 제3호A Q-analogue of hypergeometric series by Q-exponential functionsLAXMI MAJHI장전수학회 · Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집)2025 · 제28권 제4호Certain new WP-Bailey pairs and basic hypergeometric series identitiesS. Ahmad Ali, Sayyad Nadeem Hasan Rizvi대한수학회 · 대한수학회논문집2017 · 제32권 제4호

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