Certain Transformation Formulae for q-Hypergeometric Series

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2019 by IJMTT Journal
Volume-65 Issue-12
Year of Publication : 2019
Authors : Dr. Brijesh Pratap Singh
  10.14445/22315373/IJMTT-V65I12P514

MLA

MLA Style:Dr. Brijesh Pratap Singh "Certain Transformation Formulae for q-Hypergeometric Series" International Journal of Mathematics Trends and Technology 65.12 (2019):138-141 

APA Style: Dr. Brijesh Pratap Singh(2019). Certain Transformation Formulae for q-Hypergeometric Series International Journal of Mathematics Trends and Technology, 138-141.

Abstract
In present paper we have taken certain known summation formulae due to Verma and Jain and by making use of Bailey's transformation an attempt has made to establish certain beautiful and interesting transformation formulae for q-Hypergeometric series.

Reference
[1] Bailey, W.N. (1947): Some identities in Combinatory Analysis, Proc. London Math, Soc. 49, 421-435.
[2] Singh, U.B. (1994): A Note on a Transformation of Bailey, Quart, J. Math oxford (2) 45; 111-116.
[3] Verma, A. and Jain V.K. (1983): Certain Summation Formulae for q-series, J. Indian Math, Soc. 47, 71-85.
[4] Slater, L.J. (1966): Generalized Hypergeometric functions, Cambridge University Press, Cambridge.
[5] Verma, A. (1972): Some Transformation of series with arbitrary terms Institute Lambardo (Rend. SC) A 106 (342-353).
[6] Exton, H. (1983), q-Hypergeometric Functions and Applications, Halsted Press, John Wiley and Sons, New York.
[7] Srivastava, H.M. and Karlsson, P.W. (1985), Multiple Guassion Hypergeometric Series, Halsted Press, John Wiley and Sons, New York.
[8] Andrews, G.E. and Warnaar, S.O. (2007): “The Bailey transform and False theta functions”. The Ramanujan Journal, vol. 14, no1 (173-188).

Keywords
Basic Hypergeometric series; transformation; summation formulae