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Elliptic WP-Bailey Transform and its Applications


Affiliations
1 Department of Mathematics, T.D.P.G. College, Jaunpur-222002 (UP), India
2 Department of Mathematics, S.P.D.T. College, Andheri (E), Mumbai-400059, India
     

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In this paper, idea of WP-Bailey transform has been extended to elliptic WP-Bailey transform and it has been applied to establish certain interesting summation and transformation formulas for elliptic and theta hypergeometric series.

Keywords

Elliptic Hypergeometric Series, Theta Hypergeometric Series, Wp-bailey Transform, Elliptic Wp-bailey Transform, Summation Formula, Transformation Formula.
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  • G. Gasper and M. Rahman, Basic hypergeometric series (Second Edition), Cambridge University Press, New York, 2004.
  • H. M. Srivastava, S. N. Singh, Satya Prakash Singh, Vijay Yadav, Certain Derived WP-Bailey Pairs and Transformation Formulas for q-Hypergeometric Series, Filomat, 31(14) (2017), pp. 4619-4628.
  • H. M. Srivastava, S. N. Singh, Satya Prakash Singh, Vijay Yadav, Some conjugate WP-Bailey pairs and transformation formulas for q-series, CREAT. MATH. INFORM, 24(2) (2015), pp. 199-209.
  • Satya Prakash Singh, On transformation formulae for theta hypergeometric functions, J. Ramanujan Society of Math. and Math. Sc., 3(1) (2014), pp.53-62.
  • Satya Prakash Singh, On a transformation formula for elliptic hypergeometric series, South East Asian J. Math.& Math. Sc., 10(2) (2011), pp. 79-87.
  • S. N. Singh, Satya Prakash Singh, Vijay Yadav, On Bailey’s Transform and Expansion of Basic Hypergeometric Functions-II, South East Asian J. of Math.& Math. Sci., 11(2), (2015), pp. 37-46.
  • S. O. Warnaar, Extensions of the well-poised and elliptic well poised Bailey lemma, Indag Math. (N.S.) to appear at XIV. Math: CA/0309241.
  • V. P. Spiridonov, An elleptic extension of the Bailey chain, Int. Math. Res. Notices, 37 (2002), pp. 1945-1977.

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  • Elliptic WP-Bailey Transform and its Applications

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Authors

Satya Prakash Singh
Department of Mathematics, T.D.P.G. College, Jaunpur-222002 (UP), India
Vijay Yadav
Department of Mathematics, S.P.D.T. College, Andheri (E), Mumbai-400059, India

Abstract


In this paper, idea of WP-Bailey transform has been extended to elliptic WP-Bailey transform and it has been applied to establish certain interesting summation and transformation formulas for elliptic and theta hypergeometric series.

Keywords


Elliptic Hypergeometric Series, Theta Hypergeometric Series, Wp-bailey Transform, Elliptic Wp-bailey Transform, Summation Formula, Transformation Formula.

References