On transformation formulae of ordinary hypergeometric series

  • Authors

    • Keshav Yadav Department of Applied Sciences and Humanities, Faculty of Engineering &Technology, Rama University Uttar Pradesh Kanpur, Rama City, Madhana, Kanpur, 209217 Uttar Pradesh (India)
    • Adarsh Kumar DEPARTMENT OF MATHEMATICS SHIBLI NATIONAL COLLEGE AZAMGARH 276001
    • Mohd Sadiq Khan DEPARTMENT OF MATHEMATICS SHIBLI NATIONAL COLLEGE AZAMGARH 276001
    2014-07-02
    https://doi.org/10.14419/gjma.v2i3.2855

  • In this paper, making use of some well-known summation formulae and generating relations due to Qureshi, Khan and Pathan, an attempt has been made to establish some transformation formulae of ordinary hyper geometric series which are seemed to be new and in different form. We have also given some special cases.

    Keywords: Summation Formulae, Ordinary Hyper geometric Series, Transformation Formulae, Generating Relation.

    Author Biography

    • Adarsh Kumar, DEPARTMENT OF MATHEMATICS SHIBLI NATIONAL COLLEGE AZAMGARH 276001
      Research Scholar Department of MathematicsSHIBLI NATIONAL COLLEGE AZAMGARH

  • References

      1. Bailey, W. N., Generalized Hypergeometric Series, Cambridge Univ. Press, London, 1935.
      2. Bailey, W. N., Some identities in combinatory analysis, Proceedings of the London Mathematical Society, 49(2), (1947) pp. 421425.
      3. Slater, L. J., A new proof of Rogerss transformations of infinite series, Proceedings of the London Mathematical Society, 53, (1951) pp. 460475,
      4. Slater, L. J., Further identities of the Rogers-Ramanujan type, Proceedings of the London Mathematical Society, 54(1952) pp. 147167.
      5. Rainville, E. D., Special Functions, MacMillan, New York, 1960.
      6. Slater, L. J., Generalized hypergeometric functions, Cambridge University Press, Cambridge, 1966.
      7. Andrews, G. E., A general theory of identities of the Rogers-Ramanujan type, Bulletin of the American Mathematical Society, 80(1974), pp. 10331052.
      8. Andrews, G. E., An analytic generalization of the Rogers-Ramanujan identities for odd moduli, Proceedings of the National Academy of Sciences of the United States of America, 71(1974), pp. 40824085.
      9. Verma, A. and Jain, V.K.,Transformations between basic hypergeometric series on different bases and and identities of Rogers-Ramanujan type, Journal of Mathematical Analysis and Applications,76( 1), (1980)pp. 230269,.
      10. Verma, A. and Jain, V.K., Transformations of non-terminating basic hypergeometric series, their contour integrals and applications to Rogers-Ramanujan identities, Journal of Mathematical Analysis and Applications,87(1),(1982) , pp. 944.
      11. Gasper, G. and Rahman, M., Basic Hypergeometric Series, Encyclopaedia of Mathematics and Its Applications, Cambridge University Press, New York, NY, USA, 1991
      12. Singh, U. B., A note on a transformation of Bailey, The Quarterly Journal of Mathematics, 2(45)(1994),pp.111-116.
      13. Agarwal, R. P., Resonance of Ramanujans Mathematics, Vol .I, New Age International, New Delhi, India, 1996.
      14. Singh, S.P., Certain transformation formulae for q-series, Indian J. Pure Appl. Math., 31 (10), (2000), pp.1369-1377.
      15. Qureshi, M.I., Khan,M.S. and Pathan, M.A. "Some Families of Gaussian Hypergeometric Generating Relations." Proceedings of the Third Annual Conference of the Society for Special Functions and Their Applications: Varanasi (India), March 4-6, 2002: Dedicated to Prof. Brij Mohan. Society for Special Functions and their Applications, 2002.
      16. Denis, R. Y., Singh, S. N. and Singh, S. P., On certain transformation formulae for abnormal q-series, South East Asian Journal of Mathematics and Mathematical Sciences,1(3)(2003)pp.7-19.
      17. Denis, R. Y., Singh, S. N. and Singh, S. P., Certain transformation and summation formulae for q-series Italian Journal of Pure and Applied Mathematics, N (27), (2010) pp.179-190. http://ijpam.uniud.it/online_issue/201027/14-Denis-Sinhg-Singh.pdf.
      18. Srivastav, P. and Rudravarapu, M., On certain transformation formulae for polybasic hypergeometric series, ISRN Algebra, vol. 2011, Article ID 248519, 10 pages, 2011. doi:10.5402/2011/248519 (2011).
      19. Singh, S., On certain transformation formulae for ordinary hypergeometric series,International Jr. of Special Functions and Applications, 1(1) (2013) pp.9-18.

  • Downloads

  • How to Cite

    Yadav, K., Kumar, A., & Khan, M. S. (2014). On transformation formulae of ordinary hypergeometric series. Global Journal of Mathematical Analysis, 2(3), 98-104. https://doi.org/10.14419/gjma.v2i3.2855