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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 57 | Number 2 | Year 2018 | Article Id. IJMTT-V57P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V57P518

On Transformation Formulae for Basic Hypergeometric Functions by using WP Baley’s Pairs


Akash Kumar Srivastava, Neera A. Herbert
Abstract

In this paper making use of well known WP Bailey’s Pairs, an attempt has been made to established certain interesting transformation formulae for Basic Hypergeometric functions.

Keywords
Bailey’s transform, Bailey Pairs, WP Bailey Pairs, transformations formulae.
References

[1] Andrews, G.E. and Berndt, B.C., Ramanujans Lost Notebook, Part I, Springer, 2005.
[2] Denis, R. Y. : Certaian Transformation and Summation Formulae for q-Series, Italian J. of Pure and Applied Mathematics-N. 27, pp 179-190, 2010.
[3] Gasper, G. and Rahaman, M., Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1991.
[4] Laughlin :J.M., Some identities between basic hypergeometric series deriving from a new Bailey type transformation, The J.of mathematical Analysis and Applications, 345(2), pp 670-677, 2008.
[5] Laughlin :J.M. and Zimmer, P., Some applications of a Bailey-type transformations International Mathematical Forum, No. 61,pp 3007-3022, 2010.
[6] Mishra, B. P. ,On summation and transformation formulae for basic hypergeometric series, J.of Ramanujan Society of Math.and Math. Sc.Vol.2, No.1, pp.53-72, 2013.
[7] Singh, S.N., Baiey transform, WP-Bailey pairs and q-series transformations, J.of Ramanujan Society of Math. and Math. Sc.Vol.2, No.1, pp.85-92, 2013.
[8] Slater, L. J., Generalized Hypergeometric Function, Cambridge University Press, Cambridge, 1996 .

Citation :

Akash Kumar Srivastava, Neera A. Herbert, "On Transformation Formulae for Basic Hypergeometric Functions by using WP Baley’s Pairs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 57, no. 2, pp. 122-127, 2018. Crossref, https://doi.org/10.14445/22315373/IJMTT-V57P518

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